# Questions on Geometry: Volume, Metric volume answered by real tutors!

Algebra ->  Volume -> Questions on Geometry: Volume, Metric volume answered by real tutors!      Log On

Question 994450: if the length and width of a box remain constant and the height of a box gets larger how would the volume of the box change?
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
if the length and width of a box remain constant and the height of a box gets larger how would the volume of the box change?
-----------------
It would get larger.

Question 994372: In the figures below, the cube-shaped box is 6 inches wide and the rectangular box is 10 inches long, 4
inches wide, and 4 inches high. How much greater is the volume of the cube-shaped box than the
rectangular box?
End of exam
A. 66 cubic inches
B. 56 cubic inches
C. 50 cubic inches
D. 60 cubic inches

Answer by rothauserc(2272)   (Show Source):
You can put this solution on YOUR website!
Volume of cube is 6^3 = 216 cubic inches
volume of rectangular box = 10 * 4 * 4 = 160 cubic inches
216 - 160 = 56 cubic inches
***********************************************************

Question 994176: If I got a 10 kg iron circle and its thickness is 1 cm how its diameter would be ?
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
Density of iron=7.874 grams/cm^3
.

For a disk:(r=radius, h=thickness)

The radius is 20.1 centimeters.
Diameter=2 x radius=2(20.1cm)=40.2 centimeters.
.
ANSWER: The diameter is 40.2 centimeters.
.
CHECK:

.
Mass=volume x density

Question 993240: A can contains 3 tennis balls tightly packed. Each ball has a diameter of 2.5 inches. How much greater is the circumference of the can than the height of the can?

Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
Each ball has a diameter of 2.5 inches
Circumference = Pi x diameter
Circumference = Pi x 2.5
Circumference = 7.85 inches (2 decimal places)
Height = 3 x 2.5
Height = 7.5 inches
Circumference - Height
7.85 - 7.5 = 0.35 inches
Hope this helps :-)

Question 993409: The diameter of a ball is 6-1/2 inches. I want to put 3 balls into a cylinder, what are the dimensions and the volume of the cylinder for the 3 balls?
Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
If the ball has a diameter of six and a half inches.
Then the cylinder would have a radius of three and a quarter inches
and a height of nineteen and a half inches
Volume = Pi x r^2 h
Volume = Pi x 3.25^2 x 19.5
Volume = 647.1 inches^2
Hope this helps :-)

Question 993386: Box1 of dimension 30cm*40cm*120cm so what is the maximum length of the box2 in cm that we can placed inside that box1

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Box1 of dimension 30cm*40cm*120cm so what is the maximum length of the box2 in cm that we can placed inside that box1
---------------
Depends on the dimensions of box 2.

Question 993355: One dimension of a cube is increased by 1 inch to form a rectangular block. Suppose that the volume of the new block is 150 cubic inches. Find the length of an edge of the original cube.
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
One dimension of a cube is increased by 1 inch to form a rectangular block. Suppose that the volume of the new block is 150 cubic inches. Find the length of an edge of the original cube.
=======================
s*s*(s+1) = 150

s = 5

Question 993155: How many grams of water is in a box with a mass of 2400 ml
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
Hey,
2400 ml is not a mass !

It is a volume !!   Be accurate !

----------------------------------------------------------------------------
How many grams of water is in a box with a volume of 2400 ml?
----------------------------------------------------------------------------

2400 gram.

Question 993071: I make one bag size is 79×106×110cm(external) and 75×102×106cm, cone ht.Bottom is 50cm. I want separate spout attach size is diameter is 45cm and ht. Is50cm.how much cut the cone of cloth for attach the spout.

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
I make one bag size is 79×106×110cm(external) and 75×102×106cm, cone ht.Bottom is 50cm. I want separate spout attach size is diameter is 45cm and ht. Is50cm.how much cut the cone of cloth for attach the spout.
-----
Area of surface of cone = (1/3)pi*r*h
---
= (1/3)pi*22.5*50 = 1178.01 cm^2
---
Since the circumference of the bottom is pi*22.5 = 70.68 cm,
you need a piece at least 71 cm wide and 50 cm high.
---------------
Cheers,
Stan H.

Question 991744: If a hole is 600 ft deep and 28" wide how much water can fit in it
Answer by Fombitz(25151)   (Show Source):
You can put this solution on YOUR website!
First convert to consistent units, either inches or feet.

So then model the hole as a cylinder.

Question 992748: square base; s = 6.5 cm h = 8 cm what is the volume?
Answer by farohw(153)   (Show Source):
You can put this solution on YOUR website!

A pyramid has a square base. Let s = 6.5 cm h = 8 cm.

To find the volume (V) we apply the formula:

V = 112.667 cm^3

Question 992478: he Norman window illustrated below has a semicircular section on top of a rectangle. The radius of the semicircle is x. The long side of the rectangle is three times the radius of the semicircle.
Express the total area of the window, A, as a function of x.
Express the outer perimeter of the window, P, as a function of x.

Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
he Norman window illustrated below has a semicircular section on top of a rectangle.
The radius of the semicircle is x.
The long side of the rectangle is three times the radius of the semicircle.
:
Express the total area of the window, A, as a function of x.
A = + (3x*2x)
A = +
Express the outer perimeter of the window, P, as a function of x.
P = + (2(3x)+2x)
p = + 8x

Question 992485: An open box is made from a square piece of cardboard 46 inches on a side by cutting identical squares from the corners and turning up the sides.
Express the volume of the box, V, as a function of the length of the side of the square cut from each corner, x.
Find the domain of V.

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Try this with ALL variables for values. Maybe like s=46, but keep in the variable, s.

; the base became (s-2x)*(s-2x), and the height is simply, x.

Show your finished function either "simplified" or in condensed factored form:

OR

Make the substitution for s=46 if you really want or need it, and then simplify again.

Question 992515: A solid metal cylinder with a 1.5 m diameter and a 5 m lenght is heated to 180 C from 21 C. Find the volume change 16×10-6.
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
You should give us  (give explicitly in the condition part)  the value of the coefficient of the linear or the volume thermal expansion of the metal in appropriate units.

Question 992289: A water tank measures 200cm by 150cm by 100cm. Calculate the capacity of the tank.
Intially there's water in the tank to a depth of 30cm. Calculate the initial volume of water in the tank.
A tap connected to the tank delivers water into the tank at a rate of 150cm^3 per min. Write down the formula for the volume of water in the tank after t minutes, In terms of initial volume and t.

Answer by Theo(5548)   (Show Source):
You can put this solution on YOUR website!
A water tank measures 200cm by 150cm by 100cm. Calculate the capacity of the tank.

capacity of the tank is 200 * 150 * 100 = 3,000,000 cubic cm.

---------------

Intially there's water in the tank to a depth of 30cm. Calculate the initial volume of water in the tank.

if you assume the formula for volume is length * width * height, then the height of the tank is 100 cm.

if the tank is filled with water to a depth of 30 cm, then the volume of water in the tank is 200 * 150 * 30 = 900,000 cubic cm.

-----

A tap connected to the tank delivers water into the tank at a rate of 150cm^3 per min. Write down the formula for the volume of water in the tank after t minutes, In terms of initial volume and t.

initial volume in the tank is 900,000 cubic cm.

tap fills the tank at a rate of 150 cubic cm per minute.

formula would y = 900,000 + 150 * t.

t represents the number of minutes.
y represents the volume of water in the tank after t minutes.

-----

EXTRA

how long would it take to fill the tank?

set y = 3,000,000 and the formula becomes:

3,000,000 = 900,000 + 150 * t.
subtract 900,000 from both sides of the equation to get:
2,100,000 = 150 * t.
divide both sides of the equation by 150 and solve for t to get:
t = 2,100,000 / 150 which get you:
t = 14000 minutes.

Question 991862: If the diameter of the red marble is 3.0 cm, and by using the formula for volume, what is a good approximation of its volume?
cm3

Found 2 solutions by MathLover1, Fombitz:
Answer by MathLover1(11324)   (Show Source):
You can put this solution on YOUR website!

given: the diameter of the red marble is => then radius is
marble is in shape of sphere, so we have

=>approximately

Answer by Fombitz(25151)   (Show Source):
You can put this solution on YOUR website!

The exact volume would be,

A good approximation would be,

Question 991691: The volume of a cube is given by V = x3 where x is the length of a edge of the cube.The area of a square is given by A = x2, where x is the length of a side of the square. A given cube has a volume of 1728 cubic inches

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Do you have a question?

Question 991414: 225 km square, rainfall =32 cm what is the volume of water that fell in this area. thank you

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
225 km square, rainfall =32 cm what is the volume of water that fell in this area.
-------------
32 cm = 0.32 m = 0.00032 km
----
Vol = 225*0.00032 cubic km
= 0.072 cubic km

Question 991068: A cylindrical silo is 100feet hight and radius of 14 feet
How many cubic feet of grain can be kept in the silo.

Answer by MathLover1(11324)   (Show Source):
You can put this solution on YOUR website!

if cylindrical silo is hight and radius of , to find
how many cubic feet of grain can be kept in the silo find the volume

so, cubic feet of grain can be kept in the silo

Question 990729: Mona filled the glasses shown below completely with water. The total amount of water that Mona poured into the glasses is 100 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale.
http://learn.flvs.net/webdav/assessment_images/educator_mjprealgebra_v16/mjprealgebra_pretest_m3_g17_p.jpg

2.6 centimeters
4.8 centimeters
5.6 centimeters
7.4 centimeters

Answer by MathLover1(11324)   (Show Source):
You can put this solution on YOUR website!

gl.1----------
=>
gl2----------
=>

=>
=>
=>
=>

Question 990690: A cone shaped cup is used to fill a cylindrical container. The cup has the same height and radius as the container. By calculating the volume of the cone and the cylinder, find the number of times that the cone shape cup can completely fill the cylindrical container.
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
The volume of a cone is (one third) of the volume of a cylinder which has the same height as the cone and the same base radius as the cone.

So, you need 3 (three) volumes of cone to fill the cylinder.

WITHOUT calculations.

Question 990611: A 3cm cube holds 459 grains of rice.How many grains of rice would fit in a box with dimensions 9cm×3cm×4cm?
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!

Simplify this ratio:
3cm cube holds 459 grains of rice

Your box is .

A simple proportion can be used.
Using g for how many grains in the box,

Question 990351: if the area of the flattened is 20 sq in and the distance around the top of the cylinder is 4 in how tall is the tube
Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
If the area is flattened = 20 sq ins
Distance around top = 4 ins.
20 sq ins /4 ins = 5 ins (this is the height
as height x length = area)
Tube height = 5 ins.
Hope this helps :-)

Question 990399: A company makes wax candles shaped like rectangular prisms. Each candle is
7cm
long,
2cm
wide, and
10cm
tall. If the company used
5740cm3
of wax, how many candles did they make?

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Multiply the length times the width times the height of one candle to find the volume of one candle. Then divide the total volume of wax used by the volume of one candle.

John

My calculator said it, I believe it, that settles it

Question 990133: A cylinder and a right cone have the same height and radius. The volume of the cylinder is 60cm3. Determine the volume of the cone
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
20 cc
===============
Do you know how I know?

Question 989504: a rectangular container with length 4x cm, breadth 3x cm and height x cm, contains 12 identical cylindrical cans with diameter x cm and height x cm.The remaining space is filled with sand.
What is the volume of the sand that is required?leave your answer in terms of pi

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

The volume of the box is the length times the width times the height. The volume of one of the cans is , so the volume of all 12 cans is . Don't forget that you are given the diameter so you have to divide by 2 to find the radius.

Calculate the volume of the box. Calculate the volume of the 12 cans. Subtract the volume of the cans from the volume of the box. The answer is probably best presented as a binomial factor times

John

My calculator said it, I believe it, that settles it

Question 989330: A pipe 11 m long and of radius r = 5 cm is to be coated by insulation material to a thickness of δr = 1 mm. Approximate the volume δV of insulation material required in m^3. Please use Pi for π (rather than a decimal approximation) in your answer.
I answered with: pi * 0.05^2 * 11
And received the following feedback:
The idea here is to use calculus to estimate the change in volume of the pipe in adding the insulation dV/dr ·δr ≈ δV
THANK YOU

Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!
They have provided the value of δr, which is 1. We also know that r = 5 and h = 11

We need to calculate dV/dr

Use calculus to differentiate V = pi*r^2*h with respect to r to get

V = pi*r^2*h
dV/dr = 2*pi*r*h

Now plug in the given values

dV/dr = 2*pi*r*h
dV/dr = 2*pi*5*11
dV/dr = 110pi

So dV/dr ·δr is equal to

dV/dr ·δr = 110pi*1 = 110pi

The approximate value of δV is 110pi

Question 989229: A boiling company produced a cylindrical can which has a capacity of 1L. The radius of the cylinder is 2.82cm.Calculate the height of the can correct to 1 decimal place. It's an assignment I've been failing to answer this question
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

One liter is 1000 cc. The volume of a cylinder is the area of the base times the height.

So you have:

Solve for

John

My calculator said it, I believe it, that settles it

Question 989205: What is the volume of a cone with a radius of 18 cm and a height of 10 cm? Use 3.14 for pi. Round your answer to the nearest tenth.

3275.4cm^3
3391.2cm^3
3540.8cm^3
40002cm^3

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

.

Plug in your numbers and do the arithmetic.

John

My calculator said it, I believe it, that settles it

Question 989196: A tennis ball has a radius of 6.7 centimeters. What is the volume of a tennis ball? Use 3.14 for pi. Round your answer to the nearest hundredth.

157.48cm^3
1259.19cm^3
4188.79cm^3
9634.08cm^3

Answer by Alan3354(47455)   (Show Source):

Question 989130: A box measure 10 cm long 10 cm wide and 10 cm high what is its volume
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
Volume=Length x width x height
Volume=(10cm)*(10cm)*(10cm)
Volume=1000cm^3

Question 988991: how deep must be hole for tube length of 210 cm and 68 cm diameter under Ceiling of 220cm
Answer by Alan3354(47455)   (Show Source):

Question 988848: Determine the equation of the straight line through the points (-2;1) and (3;-2)
Answer by Shai(25)   (Show Source):
You can put this solution on YOUR website!
Given A(-2,1) B(3,-2)
Slope=(y2-y1)/(x2-x1)
Slope=(-2-1)/((3-(-2))
Let us represent the slope here as m
Thus the equation of the line is
m(x-x1)=(y-y1)
Henceforth,
(-3/5)(x+2)=(y-1)
Thus the equation of the line is
3x+5y+1=0

Question 988681: there is a cubic box with the volume of 29719 to the power of 3 with a mass of 950g and delivery of 14

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
That's possible.
Difficult to dispute.

Question 988130: A pipe 11 m long and of radius r = 5 cm is to be coated by insulation material to a thickness of δr = 1 mm. Approximate the volume δV of insulation material required in m^3. Please use Pi for π (rather than a decimal approximation) in your answer.
THANK YOU

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
First,  estimate the surface area of the tube.  Is is

To get the volume of the required insulation material,  multiply this surface area by the thickness of  δr = 1 mm = 0.001 m.  It gives you the answer:

δV = .δr.

Question 987995: A ball with a volume of 250 centimetres cubed is placed in a box. The box is shaped like a cube and the ball is touching the centre of each face of the cube (on the inside). Calculate the volume of empty space inside the cube
Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
A ball with a volume of 250 centimetres cubed is placed in a box.
The box is shaped like a cube and the ball is touching the centre of each face of the cube (on the inside).
Calculate the volume of empty space inside the cube.
:
Find the radius of the ball using the volume formula
= 250
multiply both sides by 3
= 750
=
= 59.6831
r =
r = 3.908 cm is radius
then
2(3.908) = 7.816 cm is the diameter, this is also the length of the side of the box
7.816^3 = 477.465 cu/cm is the volume of the box
:
477.465 - 250 = 227.465 cu/cm is the empty space around the ball in the box

Question 987579: The time it would take to empty a container whose diameter opening is 4 cm and the initial height of water is 10 cm
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
The time it would take to empty a container whose diameter opening is 4 cm and the initial height of water is 10 cm
=============
Not enough info.

Question 987649: Suppose the side length of a cube is x = 11 cm. If x changes by an amount δx = 0.01 cm, what is the corresponding approximate change in the volume of the cube δV?
THANK YOU :-)

Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

"...changes by an amount..." is non-specific. Did the measure of the edge of the cube get larger or smaller? Either one is a change, and the amount specified is a positive number does not alter the ambiguity. "approximate" without a specification of required precision is non-specific. "A little bit bigger (or smaller)" is an unassailably correct answer to this question as posed.

Be that as it may, the volume of a cube with edges that measure units has a volume of cubic units. If the measure of the edge is increased by some value , then the new volume is , and the difference between the original volume and the new volume is . Similarly, if the edge is decreased some value , then the new volume is , and the difference between the original volume and the new volume is .

Once you decide whether you are getting larger or smaller, you can plug your values of and into the appropriate expression for , do the arithmetic, and round to whatever precision you need or desire.

John

My calculator said it, I believe it, that settles it

Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!
V = x^3 ... start with the volume of a cube formula

dV/dx = 3x^2 ... apply the derivative with respect to x

dV = 3x^2*dx

dV = 3*11^2*0.01 ... plug in x = 11 and dx = 0.01

dV = 3.63

If the change in x is 0.01 cm, then the approximate change in volume is 3.63 cubic cm

-------------------------------------------------------
Alternative non-calculus based way to do it

Original Volume:
V = x^3
V = 11^3
V = 1,331

Say the side length is x=11+0.01 = 11.01 now. That makes the volume become
V = 11.01^3
V = 1,334.633301

The difference in the two volumes is
1,334.633301 - 1,331 = 3.63330099999984 which is approximately 3.63 that we got before

The same applies if you did x = 11-0.01 = 10.99 (the only real difference is that the result of the subtraction would be -3.63, but the absolute value of that leads to the same result)

Question 987648: A pipe 11 m long and of radius r = 5 cm is to be coated by insulation material to a thickness of δr = 1 mm. Approximate the volume δV of insulation material required in m^3.
THANK YOU :-)

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
First,  estimate the surface area of the tube.  Is is

= = 0.08635 .

To get the volume of the required insulation material,  multiply this surface area by the thickness of  1 mm = 0.001 m.  It gives you the answer:

0.08635*0.001 = 0.0008635 .

In cubic centimeters,  it is   = 863.5 .

Question 987640: I saw a video and thought that I understand this; well, somewhat. But I need to know if I am doing this correctly. Please, I am asked to solve for pie: V = (4/3)(pie)(r^3), solve for pie.
Thank you,
Clu

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
No math problems with pie.
Use the Greek letter pi.

Question 987570: A fish tank 60 cm long,40 cm wide and 30 cm high is three quarters full of water.All the water is poured into a second tank 75 cm long and 24 cm wide.Find the height of water in the second tank.

Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
A fish tank 60 cm long, 40 cm wide and 30 cm high is three quarters full of water.
Find the volume of the water in cu/cm
V = 60 * 40 * (30)
V = 2400 * 22.5
V = 54000 cu/cm
:
All the water is poured into a second tank 75 cm long and 24 cm wide.
Find the height of water in the second tank.
let h = the height of the water in this tank
h * 75 * 24 = 54000
1800h = 54000
h = 54000/1800
h = 30 cm is the height of the water in this tank

Question 987597: Calculate the dimention of a box if the volume is 29791,mass is 950g and the number of a box is 14

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Makes no sense.
===============
If you post it again, it will still make no sense.

Question 987588: Calculate the dimention of a box if the volume is 29791,mass is 950g and the number of a box is 14.
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Makes no sense.