A square prism & a cylinder have the same volume of 832mm cb. Which is greater?

Question

the base edge of the prism or the diameter of the base?

oh A square prism & a cylinder have the same height of 13mm & the same volume of 832mm cb .

yes diameter of the base of the cylinder

Answer 1

Without knowing the height of the cylinder, there is no way to answer this question. It's also not clear if "square prism" means a cube, or just a prism with a square base. If it's a cube with edge length s and a cylinder with height h equal to its diameter d, then the volume of the cube is s^3 while the volume of the cylinder is pi*((d^2)/4)*h = (pi/4)*(d^2)*d = (pi/4)*d^3. So we set them equal, (pi/4)*d^3 = s^3, and we take the cube root of both sides to get (pi/4)^(1/3)*d^3 = s^3. (pi/4)^(1/3) is less than 1, which means that d is greater than s, so the diameter of the base is greater than the edge length of the cube.

Answer 2

Only having the same volume, you cannot answer this question. If the heights are also the same, then the base areas would be equal pi*r^2 = x^2, where x is the base edge. If you solve for x, you get x=r*sqrt (pi) or x = D*sqrt (pi)/2 --> x = .886D. That means D is greater than x.
P.S. A square prism does not mean a cube, it means the base is square, but height is variable.

Answer 3

Volume of a square prism with side a and height h= V(sp) = a^2 * h
Volume of a cylinder with radius r and height h V(c) = (pi)(r^2)h

We have to assume h is the same between them in order fo ra comparison to work out. If not we have too many variables.

Since the volumes are the same...
V(c) = (pi)(r^2)h = V(sp) = a^2 * h
(pi)(r^2)h = a^2 * h (h cancels out)
(pi)(r^2) = a^2
Since diameter (d) = 2r ====> r = (d/2)
(pi)(d/2)^2 = a^2
(pi)/4 *d^2 = a^2
We see here that a is a function of d and since (pi)/4 < 1 we can deduce that the diameter d would be greater than side a.

Answer 4

The base edge of the prism is 9.4mm

The diameter of the cylinder depends on the height of the cylinder.

So the answer is yes and no