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Tutors Answer Your Questions about Volume (FREE)
Question 571299: I don't know if I submit my question correctly. Here it goes again.
What would be square feet of a room if the measurements is in inches. 115 x 160.
Thanks
Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!What would be square feet of a room if the measurements is in inches. 115 x 160.
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= (115/12) ft * (160/12) ft
= 115*160/144 sq ft
Question 571223: how many gallons does my tank hold if it is 6 feet long,18 inches wide and 22 inches tall?
Answer by Theo(2967)  (Show Source):
You can put this solution on YOUR website!we'll convert everything to inches.
the volume of your tank is equal to 72 * 18 * 22 = 28512 cubic inches.
the number of cubic inches in a gallon is equal to 231.
divide 28512 cubic inches by 231 cubic inches to get 123.4285714 gallons.
this assumes the tank is holding liquid.
there is such a thing as a dry gallon, but it is not commonly used.
a reference that discusses imperial gallon versus united states wet gallon versus united states dry gallon is shown below:
http://en.wikipedia.org/wiki/Gallon
i would assume liquid gallon unless otherwise specified, which is unlikely.
Question 571149: I need to know how to estimate the volume of a box (approximately 100 - 500 cm3) in cubic centimeters.
Answer by richard1234(4789)  (Show Source):
You can put this solution on YOUR website!Volume of a box = length*width*height.
Also, I would think that "approximately 100 - 500 cm3" is an estimate for the volume of a box in cubic centimeters.
Question 570868: a sample of sea water weighs 158 grams and has a volume of156 ml.what is the density?
Answer by Alan3354(21555) (Show Source):
Question 570840: what is the volume of a ball that has a radius of 6a?
Answer by Alan3354(21555) (Show Source):
Question 570049: If the height of a cylinder is doubled,will it's surface area also double?
Answer by richard1234(4789) (Show Source):
You can put this solution on YOUR website!Use "its" instead of "it's." Also, only the lateral surface area doubles. If the area of the base remains unchanged, the total surface area won't double (it would be between 1 and 2 times the original surface area).
Question 568826: Why would doubling the height of a pyramid double the volume?
Answer by richard1234(4789) (Show Source):
You can put this solution on YOUR website!V = (1/3)Ah where A is the area of the base. If you double the height and leave A unchanged, the volume will also be doubled (replace h with 2h in the formula).
Question 567895: Compute the volume of an icosahedron whose edge measures 3 inches.
Answer by bucky(2097) (Show Source):
You can put this solution on YOUR website!The volume of a icosahedron (a regular polyhedron with 20 identical equilateral triangular faces, 12 vertices, and 30 edges) is given by the formula:
.
.
in which V is the volume in cubic units and s is the length of an edge in units matching the cubic units of the volume.
.
For this problem you are given that the length of a side is 3 inches. Therefore, the volume calculated by using the formula will in units of cubic inches.
.
Start with the formula for the volume:
.
.
Substitute 3 for s to get:
.
.
Replace the  with its equivalent value of 27:
.
.
Note that the 12 in the denominator of the leading term can be replaced by 3 times 4 to result in:
.
.
Multiply the leading term by the last term (27) to get:
.
.
Divide the 3 in the denominator of the first term into the 27 in the numerator. This reduces the first term as shown:
.
.
and multiply out the numerator of the first term and you have:
.
.
and if you prefer, you can multiply the right side to have the form of the answer be:
.
.
Then by doing the distributed multiplication in the numerator you get:
.
.
The square root of 5 is an irrational number. Therefore, there is not an exact answer to this problem. However, you can approximate the answer by letting the square root of 5 equal 2.23606798. Substitute that value for the square root of 5 and the formula becomes:
.
.
Add the terms in the parentheses at it simplifies to:
.
.
Multiplying out the numerator (45*5.23606798) and then dividing by the denominator (4) gives the "approximate" answer:
.
 and its units are cubic inches
.
I hope this gives you the information you need to solve this problem.
.
Question 567893: A right pyramid has a square base and a lateral area of 144 in2. If the slant height is twice the length of a base edge, find the volume.
Answer by Theo(2967) (Show Source):
You can put this solution on YOUR website!right pyramid with square base and lateral area of 144 square inches.
slant height is twice the length of a base edge.
what is the volume?
the faces of your pyramid are the base plus 4 isosceles triangles.
the 4 isosceles triangle form the lateral area.
divide 144 by 4 and you get the area of 1 of the isosceles triangles.
the slant height of the pyramid is equal to the perpendicular bisector of that isosceles triangle.
this also makes it the height of that isosceles triangle.
the base is set to x.
the slant height is set to 2x.
the area of the isosceles triangle is 36 square inches.
the formula for the area of a triangle is bh/2 = A which can also be written as bh = 2A
since A of the triangle is 36, this formula becomes bh = 72
since b = x and h = 2x, this formula becomes 2x^2 = 72
divide both sides of this equation by 2 to get x^2 = 36
take the square root of both sides of this equation to get x = 6.
this makes the height of the triangle equal to 2x which is equal to 12.
since the height of the triangle is 12, this makes the slant height of the pyramid also equal to 12 because the altitude of one of the faces of the pyramid is the slant height of the pyramid.
you can now find the height of the pyramid by extending a line from the foot of one of the heights of one face of the pyramid to the foot of the height of the opposite face of the pyramid.
this forms another isosceles triangle with the equal sides being 12 and the base being 6.
you can now find the height of the pyramid which will be equal to sqrt(135)
you can now find the volume of the pyramid because the volume of the pyramid equals b^2h/3.
b is equal to 36*sqrt(135)/3 which is equal to 12*sqrt(135).
the decimal equivalent would be 139.4274005
check the diagram to see what i'm talking about.
in that diagram, EG is one of the slant heights of the pyramid and is also the height of the triangular face formed by DEC.
if you slice across the middle of the base of the pyramid, you form another triangle called EHG which has a base of 6 and equal legs of 12. these equal legs are EG and EH. since EG equals 12, then EH equals 12 also.
use pythagorean formula to find EF which is the altitude of the pyramid.
once you find that, you have the volume of the pyramid because that is equal to 1/3 * the height of the pyramid times the area of the base which winds up being 1/3 * sqrt(135) * 36.
Question 567676: An astronaut in her spacesuit weighs 330lb on Earth. What would her weight be on the moon?
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!An astronaut in her spacesuit weighs 330lb on Earth. What would her weight be on the moon?
--------------
What's the gravitional acceleration on the moon?
Question 567647: A fish tank measures 0.40 meters long. What is the length of the tank in millimeters?
Answer by Alan3354(21555) (Show Source):
Question 567613: The volume of the sphere is 10 cm^3. If the radius of the sphere is doubled, what is the volume of the sphere?
Answer by Alan3354(21555) (Show Source):
Question 567316: I have a box that measures 3m x 3m x 3m. What is the volume of the cube?
Answer by Maths68(1140)  (Show Source):
Question 567322: The volume of a right circular cylinder is 540 cubic centimeters express the height of the cylinder as a function of its radius r?
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!The volume of a right circular cylinder is 540 cubic centimeters express the height of the cylinder as a function of its radius r?
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 , h & r in cms
Question 567196:
Answer by nottohave(4)  (Show Source):
Question 566576: A grain silo has a cylindrical shape. Its diameter is 16 ft, and its height is 46ft. What is the volume of grain that can be stored in the silo?
(Use the value for , and round your answer to the nearest cubic foot. Be sure to include the correct unit in your answer.)
Answer by ankor@dixie-net.com(12686)  (Show Source):
You can put this solution on YOUR website!A grain silo has a cylindrical shape.
Its diameter is 16 ft, and its height is 46ft.
What is the volume of grain that can be stored in the silo?
;
radius of silo will be 8 ft
Vol of cylinder: 
therefore:
V = 9248.85 ~ 9,249 cu/ft
Question 566762: Rectangular solid (6, 8, 10in) find the Volume
Answer by jim_thompson5910(21667) (Show Source):
Question 566216: a box holds 10 cubes of 2 inches cubed. How big is the box?
each cube volume 8 cu.inches
total volume is 80 cu.in.
hence the volume of thebox should be at least 80 cu.in
cube rooting 80 we will get 4 < (cube root of ) 80 < 5
we cannot have 4. something for a side in the cube .
so we take 5 as the box side
so the box size is minimum of 5 inches
cheers
Found 2 solutions by anyDoubt, Alan3354:
Answer by anyDoubt(1) (Show Source):
You can put this solution on YOUR website!each cube volume 8 cu.inches
total volume is 80 cu.in.
hence the volume of the box should be at least 80 cu.in
cube rooting 80 we will get 4 < 80^(1/3) < 5
we cannot have 4 and a fraction for a side in the cube .
so we take 5 as the box side
so the box size is minimum of 5 inches
cheers
Answer by Alan3354(21555) (Show Source):
Question 565825: A Pyramid has a volume of 100cm cubed and a height of 24cm. How can I find the area of its base?
Answer by solver91311(12118)  (Show Source):
Question 565667: How do you make a cylinder with radius 4 and height 5
Answer by Alan3354(21555) (Show Source):
Question 565482: how many cubic feet in a 12inch by 18 inch cylinder This will be filled with concrete
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!how many cubic feet in a 12inch by 18 inch cylinder This will be filled with concrete
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Which is the diameter? or radius?
Question 565457: PLease help me!!! i have no clue what i am doing. Please help me. and thank you!!(:
If a regulation NBA basketball has a circumference of 29.5 inches, then findthe following:
diameter:
radius:
surface area:
volume:
Answer by scott8148(5879)  (Show Source):
You can put this solution on YOUR website!the diameter is the circumference divided by pi (3.14159...)
the radius is half of the diameter
the surface area is 4, times pi, times the radius squared
the volume is 4/3, times pi, times the radius cubed
Question 565107: The formula for the volume of a cone is  , where V represents the volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 110 cubic centimeters and with at radius of 5 centimeters?
Answer by kingme18(97)  (Show Source):
You can put this solution on YOUR website!First, we'll plug the volume and radius into the formula:
Simplify the right hand side by typing  into a calculator (you get approximately 26.17, if you use 3.14 for pi):
Divide both sides by 26.17 to finish getting h by itself:
The height is approximately 4.2 cm.
Question 564691: A cylinder has a volume of 1200cm3 and the least surface area possible. What are the dimensions of the cylinder?
Answer by richard1234(4789) (Show Source):
You can put this solution on YOUR website!Assume the cylinder has a circular base. We want to minimize
 , given  . Couple ways to do this:
Solution 1: Let  . Then  = 2\pi r^2 + \frac{2400}{r}) . Taking derivative with respect to r,
 . This equals zero when  , or when  . ∎
Solution 2: Using the method of Lagrange multipliers, there exists a constant  with A(r,h) and V(r,h) such that
 , therefore
Equating these two,
 , finding the actual dimensions follows. ∎
There are probably other solutions involving AM-GM inequality or other techniques. The preferred solution to use is probably dependent on the course you are taking.
Question 564297: Suppose that a box has a volume of 100 Cubic centimeters and that the area of the bottom of the box is 50 square centimeters. Find the height of the box.
Answer by ad_alta(170)  (Show Source):
You can put this solution on YOUR website!Let 'h' be the height. We know the volume (V) is constrained by the equation V=Ah for a base area 'A.' Thus, 100=50h. The height must therefore be 2 cm (100/50=2).
Question 563940: Find the volume of a sphere with a 6-foot diameter. Use 3.14 for π
Answer by Alan3354(21555) (Show Source):
Question 563851: Using the Pythagorean Theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long.
A. 4√ 41
B. 6
C. 12.81
D. 36
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!Using the Pythagorean Theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long.
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Question 563725: round off the square feet calculated in number 20 to the nearest hundred square feet.
Answer by Alan3354(21555) (Show Source):
Question 562774: what is the volume of a box that is 14 cm long, 10 cm wide, and 3 cm high?
Answer by mananth(10541)  (Show Source):
Question 562335: I have two aquariums. One is 12x18x30. The other is 13x24x30. how many gallons of water will fit into each of them.
Answer by mananth(10541) (Show Source):
You can put this solution on YOUR website!I presume they are in feet
One is 12x18x30.
Volume = L*W*H
12x18x30=6480 cu.ft
The other is 13x24x30
=9360
9360+6480 =14840 cu.ft
1 cu.ft = 7.48 gallons
14840/7.48= 1984 gallons ( rounded off)
Question 562264: a cylindrical tin if height 15cm and radius 4cm is filled with sand from a rctangular box. how many times can the tin be filled if the dimensions of the box are 50cm by 40cm by 20cm?
Answer by mananth(10541) (Show Source):
You can put this solution on YOUR website!Volume of Box / volume of tin = number of tins required
Volume of box =50*40*20= 40000 cu.cm
Volume of Tin = pi*r^2*h=pi*4^2*15 = 754 cu.cm
4000/754= 53 tins (rounded off)
Question 561430: What is the volume for a cylinder with a radius of 14 inches and a height of 1.5 feet?
Answer by Alan3354(21555) (Show Source):
Question 560663: What are the demensions of a 180 sqare foot cone
Answer by unlockmath(1120)  (Show Source):
You can put this solution on YOUR website!Hello,
We're missing some data before we can solve this.
The formula for volume of a cone is:
1/3 Base times Height or
1/3 Pi times radius squared times base.
We need at least the height or base or radius before this can be solved.
RJ
www.math-unlock.com
Question 560526: okay, after several attemps, and an hour later.. I still need help. I am asked to write a polynomial for the volume of the region between the small cylinder and the larger cylinder. The smaller cylinder is inside the larger and the only information I have is: the smaller cylinder has a radius of 3, and both cylinders have a height of 6r. The radius of the larger cylinder is represented by a "r". Thank you!
Answer by mananth(10541) (Show Source):
You can put this solution on YOUR website!Larger cylinder
radius = r
length = 6r
Volume = pi * r^2 *6r
= 6pir^3
Volume of smaller cylinder
radius = 3
length = 6r
Volume = pi*3^2*6r
=54pir
Volume of region between them =
6pir^3-54pir
m.ananth@ hotmail.ca
Question 560484: I am asked to write a polynomial for the volume of the region between the small cylinder and the large cylinder. The radius of the larger cylinder is 3 and the height of both cylinders is 6r.
Answer by solver91311(12118) (Show Source):
You can put this solution on YOUR website!
Not enough information. You didn't share the radius of the smaller cylinder, nor did you confirm that the smaller cylinder is wholly contained within the larger cylinder (or if not wholly contiained, some data that would allow computation of the proportion of the smaller cylinder that is within the larger.
John
My calculator said it, I believe it, that settles it
Question 560288: how many bricks each measuring 25cm*11.25cm*6cm will be needed to build a wall 8m long,6m high, 22.5 m thick?
Answer by mananth(10541) (Show Source):
You can put this solution on YOUR website!volume of wall / volume of each brick = number of bricks
Volume of wall = 8m*6m *22.5 m =1080 m^3
Volume of each brick = 25cm*11.25cm*6cm
convert to meters
0.25*0.1125*0.06=0.0016875 m^3
1 080 / 0.0016875 = 640,000 bricks
Question 560093: a company that manufactures dog food wishes to pack the food in closed cylindrical tins what should be the dimensions of each tin of each is to have a volume of 128
Answer by solver91311(12118) (Show Source):
You can put this solution on YOUR website!
Impossible to tell. There are infinite answers to this question as posed. You need an additional constraint such as a fixed radius, a fixed height, or perhaps the requirement to minimize the surface area (i.e., make the can as cheaply as possible.)
John
My calculator said it, I believe it, that settles it
Question 559510: a rectangular solid has length 2 feet, width 18 inches, and height 1 foot. what is the volume of this solid, in cubic feet?
Answer by josmiceli(6778)  (Show Source):
Question 559442: Volume is 1350cm = Base Area 150cm x height X
Answer by mananth(10541) (Show Source):
Question 558486: explain me how to fin the lenght, width, and height this is the information they gave me.
the area of the base of the box is 20 square inches
the perimeter of the base of the box is 18 inches
the volume of the box is 160 cubic inches
Answer by ankor@dixie-net.com(12686) (Show Source):
You can put this solution on YOUR website!fin the lenght, width, and height this is the information they gave me.
Write an equation for each statement:
:
"the area of the base of the box is 20 square inches"
L * W = 20
:
"the perimeter of the base of the box is 18 inches"
2L + 2W = 18
simplify, divide by 2
L + W = 9
L = (9-W)
:
Replace L with (9-W) in the area equation
W(9-W) = 20
-W^2 + 9W = 20
0 = W^2 - 9W + 20; a quadratic equation, that will easily factor to:
(W-4)(W-5) = 0
two solutions
W = 4, then L = 5
W = 5, then L = 4
:
"the volume of the box is 160 cubic inches"
Find the height by dividing the volume by the area of the base (20)
 = 8 inches is the height
;
;
The dimensions of the box 5 by 4 by 8
Question 557228: If the diameter is 4 inches, and the height is 14 inches, what is the surface area of the cylinder
Answer by bluemockingjay7(41)  (Show Source):
You can put this solution on YOUR website!formula of the surface area of the cylinder: 2(3.14)rh
diameter = 4/2 = 2 = radius
height = 14
Solution:
surface area=2(3.14)(2)(14)
surface area=2(3.14)(28)
surface area=2(87.92)
surface area=175.84 square inches
Question 556979: A company produces cardboard boxes with the top, bottom and sides measuring 5 feet.It costs the company 4 cents a square foot to make each box. The square footage is determined by finding the area of all six sides of the box. Find the cost to make 100 boxes.
Answer by josmiceli(6778) (Show Source):
You can put this solution on YOUR website!Each side is  ft2
The area of 6 sides is  ft2
The area for 100 boxes is  ft2
( 4 cents / ft2 ) x ( total ft2 ) = 
It costs $600 to make 100 boxes
Question 556862: If the cube above has a volume of 8 m3, what is the surface area of the cube?
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!If the cube above has a volume of 8 m3, what is the surface area of the cube?
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Find the side length, s.
The cube has 6 sides, each a square with sides = s.
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