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

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Question 30504: an open box is to be constructed from a piece of cardboard 15 inches by 25 inches by cutting squares of length x from each corner and folding up the sides. Express the volume of the box as a function of x. what is the domain v?
Click here to see answer by venugopalramana(3286)

Question 30325: please help me in my homework..i need it tomorrow..please..
the base of a pyramid is an isosceles triangle whose sides are 78cm long (each), the third side equalling 60cm. each dihedral angle at the base contains 45 degrees. find the volume of the pyramid.
Click here to see answer by Fermat(127)

Question 30833: There is a box with a square base, and a volume of 32000cm^3, with an open top, what is the least material used, and what are the dimensions?
Click here to see answer by josmiceli(9667)

Question 30899: My problem has to do with changing a sphere, with a S.A of 4536cm^2, to a volume. I know how to find the the S.A., but I am a little confused on how to change this to a volume answer. My assignment for this question is titled "Find the volume of each sphere. Round to the nearest tenth." I have a picture of a solid round shape with the indicated S.A. I mentioned above. I don't mean to rush, but I do need this asap.
Thanks for your help
Click here to see answer by mbarugel(146)

Question 31088: TI found this problem really tough... ^^U
The circles C: x^2 + y^2 + kx + (1+k)y - (k+1) = 0, pass through the same two points for every real number k
(1) Find the coordinates of these two points
(2) Find the Minimum value of the radius of a circle C
Any help would be really really appreciated!
Click here to see answer by venugopalramana(3286)

Question 31234: How do I find the volume of a pentagon?
Click here to see answer by longjonsilver(2297)

Question 31220: if the length of one side of a cube is 6x3(is cube), then what is the volume of the cube?
Click here to see answer by troyapplehelen(46)

Question 26217: 1) An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
a) Find the function V that represents the volume of the box in terms of x.
Answer

b) Graph this function.
Show Graph here

c) Using the graph, what is the value of x that will produce the maximum volume?
Answer
Click here to see answer by danirivera5(2)

Question 33095: The volume of a cylinder (think about the volume of a can) is given by V=pir^2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.
a) Write h as a function of r.
b) What is the measurement of the height if the radius of the cylinder is 2 centimeters?
c) Graph this function.

Click here to see answer by Earlsdon(6287)

Question 33291: First I had to find the volume of a cylindrical can measuring 10cm high with a radius of 4cm. The answer I found was 502cm3 rounded to the nearest whole number. Now, I need to design a rectangular box on centimeter graph paper that will have the same volume (rounded to the nearest whole number) as the cylindrical can. I know the volume of a rectangular box is lxwxh. How would I calculate the dimensions knowing the volume is equal to the cylindrical can? PLease help. I need to design 3 other rectangular boxes as well with the same volume but once I know how to design the first box, I will hopefully be able to do the others.
Click here to see answer by stanbon(57285)

Question 33554: A regular pyramid has a triangular base with a base edge of 24 inches. It's height is 36 inches. What is the volume of the pyramid?
Click here to see answer by venugopalramana(3286)

Question 33966: A box has a volume of 7500 cm3 and a surface area of 2600cm2. what are the length, width, and height of the box?
Click here to see answer by fanism(39)

Question 33966: A box has a volume of 7500 cm3 and a surface area of 2600cm2. what are the length, width, and height of the box?
Click here to see answer by xcentaur(357)

Question 34022: I'm not sure if the problem should go here but here goes...
The volume of a box with a rectangular base is 300cm cubed. The lengths of the base are 6cm and 10cm. I need to find the height of the box and the sufrace area of the box. I tried 6*10*h=300 but it didn't work. I wanted to find the area of the base in hope that it would help me but I don't know what to do after. Please help!
Thanks!
Click here to see answer by venugopalramana(3286)

Question 34692: A diagonal of a cube joins 2 vertices not in the same face. If the diagonals are 4root3 cm long, what is the volume?
Click here to see answer by stanbon(57285)

Question 34694: Find the radius of an inscribed circle in a triangle with legs 12, 12, 8.
Click here to see answer by venugopalramana(3286)

Question 35243: I need this immediately for my H.W : The total surfac area of a cone is 616 sq cm.Its slant height i.e. length is equal to three times the radius of the base.Find its radius and slant height.
Please please please send the answer fast...
Click here to see answer by venugopalramana(3286)

Question 35333: I need as quick as possible for HW: FInd the volume of a regular octahedron with sides equalling fifty square root of three cubic units? I don't know what to do please help me
Click here to see answer by venugopalramana(3286)

Question 35409: i need to know the volume measure of an triangular prism is and the amount of space is
Click here to see answer by venugopalramana(3286)

Question 35408: i need to know what the volume measures and amount of space on an object is for a rectangular prism
Click here to see answer by venugopalramana(3286)

Question 35431: How do I find the volume of a cone that has a circumfrence at the base of 100 feet and its height is 14 feet high.
Click here to see answer by Nate(3500)

Question 35765: Hi,
Can anyone answer this?
In cubic meters,how much greater is the volume of a cylinder with height 21m and a radius 12m than the volume of a square prism with height 21m and base 12m on a side?
Click here to see answer by checkley71(8403)

Question 36023: A sphere is inscribed in a cone with radius 6 and height 8. Find the volume of the sphere.
Click here to see answer by venugopalramana(3286)

Question 36302: What happens to the volume if the length is doubled, the height is doubled, and the width is tripled?
Click here to see answer by checkley71(8403)

Question 36744: A cylinder has a radius of 5 in. If the volme of the cylinder is 250π in.3, what is the height of the cylinder? [Hint: The volume of a cylinder is given by V = πr2h.]

Click here to see answer by checkley71(8403)

Question 25195: I am not sure I am doing this right, Could you please tell if this the right formula and not sure where to go from there.
An open-top box is to be constructed from a 6 by 8 foot rectangler cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
Find the V function that reprents the volume of the bos in terms of x.
Formula...V=L*W*H
Confused after that!!!!!!
Any help would be apprecited.....

Click here to see answer by stanbon(57285)

Question 37601: is the volume between a 5m sphere and a 9m sphere 2530.0292405333?
Click here to see answer by checkley71(8403)

Question 38271: If the circumference of a right circular cylinder is 18pi(don't have pi on the keyboard) and the height of the cylinder is 8, then find the volume to the nearest tenth. I found the radius of the circle to be 9, but when i find the volume of the cylinder i get 2287.1, which isn't one of my choices.
Click here to see answer by fractalier(2101)

Question 39774: An empty rectangular tank measured 50cm by 20cm and is 30cm deep.
5 litres of water was poured into the empty tank. Calculate the depth of water than in the tank.

Click here to see answer by Nate(3500)

Question 39831: I have a given volume of 300cm³. The ratio between height and radius is 1.1:1 but I can't calculate the inverse formula for the volume. Please help
Click here to see answer by venugopalramana(3286)

Question 40058: A rectangle has sides of 3x – 4 and 7x + 10. Find the expression that represents its perimeter.

Click here to see answer by fractalier(2101)

Question 40509: What is the Exit-Level Mathematics chart?

Click here to see answer by rajagopalan(158)

Question 40668: Question
A solid pyramid of height 40 cm and with a square base of sides 30 cm each is put into a cubical tank of sides 40 cm each. The tank is then filled with water. If the pyramid is removed, find the depth of water in the tank.
Please help to solve this question.
Thank you very much.
Click here to see answer by Nate(3500)

Question 41446: Question
A rectangular tank has a base 60 cm by 20 cm. A solid metal pyramid with base of sides 10 cm each and height 27 cm is placed inside the tank. The tank is then filled with water until it completely covers the pyramid. If the pyramid is removed, calculate the fall in the level of water in the tank.
My teacher had given the answer as 3/4 cm or 0.75 cm. He wanted us to try to do it.
I have obtained the same answer and I don’t seem to be able to explain it. Perhaps, you can tell me what I have done is correct.
Let the fall in the level of water in the tank = h
Volume of the tank
= base x height
= 60 x 20 x h
= 1200 h
Volume of the pyramid
= 1/3 x base area x height
= 1/3 x 10 x 10 x 27
= 900
What I did was :-
Volume of the tank = Volume of the pyramid
1200h = 900
h = 900/1200
h = 3/4
I find the way I did it unexplainable. What do you think ? Please help. Thanks.
Click here to see answer by venugopalramana(3286)

Question 16621: Write 144 lb to 48 lb as a ratio in simplest form using a colon.
Click here to see answer by fractalier(2101)

Question 44294: my math teacher says that the columne of a cubic centimeter is the same as the columne of a cubic millimeter, and the same as the volumne of a cubic inch. How is this possible? Thank You. Paula
Click here to see answer by adamchapman(301)

Question 44476: The volume of a cylinder is given by where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.
A) Write h as a function of r.
For this problem I got I am not sure if this is correct or not.
B) Graph the function. I am not sure how I am supposed to graph this
Click here to see answer by Earlsdon(6287)

Question 44474: An open-box top is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out.
A) Find the function V that represents the volume of the box in terms of x.
B) Graph this function and show the graph over the valid range of the variable x.
C) Using the graph, what is the value of x that will produce the maximum volume?
I have been struggling with this problem all week if it wasn't for this problem my assignment would be done. Please help if you can thanks!!!
Click here to see answer by venugopalramana(3286)

Question 44473: An open-box top is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out.
A) Find the function V that represents the volume of the box in terms of x.
B) Graph this function and show the graph over the valid range of the variable x.
C) Using the graph, what is the value of x that will produce the maximum volume?
I have been struggling with this problem all week if it wasn't for this problem my assignment would be done. Please help if you can thanks!!!
Click here to see answer by venugopalramana(3286)

Question 44472: An open-box top is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out.
A) Find the function V that represents the volume of the box in terms of x.
B) Graph this function and show the graph over the valid range of the variable x.
C) Using the graph, what is the value of x that will produce the maximum volume?
I have been struggling with this problem all week if it wasn't for this problem my assignment would be done. Please help if you can thanks!!!
Click here to see answer by venugopalramana(3286)

Question 44454: The volume of a cube is given by V = s3. Find the length of a side of a cube if the Volume is 1000 cm3.
Click here to see answer by checkley71(8403)

Question 44562: What is the measurement of the height if the radius of the cylinder is 2 centimeters?
Click here to see answer by Nate(3500)

Question 44745: Dear Sir,
MY friend had done this but I can't really understand what he had written.
The cross-section of a drain is a rectangle 30 cm wide. If the water 3.5 cm deep flows along the drain at a rate of 22 cm per second, how many litres of water will flow through each minute ?
Volume = width x depth x height
(width and depth are given namely 30 and 3.5 as for the height is the water flows along the drain is consider its length, in this case, 22 ? (Am I right ?)
If this is true, volume per second = 30 x 3.5 x 22 = 2310 cm^3
Therefore, volume per minute = 2310 x 60 = 138600
Since the answer is required in litres thus 138600 cm^3 = 138 600/1000 = 138.6 litre.

Thank you.
Click here to see answer by stanbon(57285)

Question 44741: My Question
A trough, in the form of an open rectangular box, is 1.85 m long, 45 cm wide and 28 cm deep externally. If the trough is made of wood 2.5 cm thick, find, in cubic centimetres, the volume of wood used.
Thank you in anticipation.
Click here to see answer by venugopalramana(3286)

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