Question

A cone and a pyramid have the same height and same volume. If the radius of the base of the cone is r, what is the side length of the square base of the pyramid

Answer 1

Answer:

The answer is D r squareroot π

Step-by-step explanation:

The formula for the volume of a cone and a pyramid is the same: V = 1/3 Bh. Since the cone and the pyramid have the same volume and height, we just need to set the area bases equal to solve for the side length of the square base.

Answer 2

Answer:  The answer is 1.772 r.

Step-by-step explanation:  Given that a cone and a pyramid have the same height and same volume. The radius of the base of the cone is 'r' units.

We are to find the side length of the square base of the pyramid.

Let, 'h', be the height of both cone and pyramid and 'l' be the side length of the square base of the pyramid.

Then, the volumes of both cone and pyramid are respectively

$V_c=\dfrac{1}{3}\pi r^2h,\\\\V_p=\dfrac{1}{3}l\times l\times h=\dfrac{1}{3}l^2h.$

Since the volume of cone is equal to the volume of pyramid, so we have

$V_c=V_p\\\\\Rightarrow \dfrac{1}{3}\pi r^2h=\dfrac{1}{3}l^2h\\\\\Rightarrow \pi r^2=l^2\\\\\Rightarrow l^2=\pi r^2\\\\\Rightarrow l=\sqrt{\pi}r\\\\\Rightarrow l=\sqrt{3.14}r\\\\\Rightarrow l=1.772r.$

Thus, the side length of the square base of the pyramid is 1.772 r.