Question

The volume of a cylinder is 24 pi cubic feet. What is the volume of a cone having the same base and same height

Answer 1

I believe that the radius is 2 and the height is 6
2 squared is 4 times 6 is 24 times pi would be 24 pi
1/3 pi 2^2 6
1/3 (pi)(4)(6)
1/3 (pi)(24)
8pi feet cubed, I believe
assuming you are leaving in answer in pi form.

Answer 2

Answer:

Volume of the cylinder(V) is given by:

$V = \pi r^2h$

where, r is the radius of the cylinder and h is the height of the cylinder.

Volume of a cone(V') is given by:

$V' = \frac{1}{3} \pi r'^2h'$

where,

r' is the radius and h' is the height of the cone.

As per the statement:

The volume of a cylinder is 24 pi cubic feet.

⇒ $V=24 \pi$ cubic feet.

⇒$24 \pi = \pi r^2h$                     ....[1]

To find the volume of a cone having the same base and same height.

⇒r = r' and h = h'

then;

$V' = \frac{1}{3} \pi r'^2h'$

⇒ $V' = \frac{1}{3} \pi r^2h$

⇒ $V' = \frac{1}{3} (24\pi)$           using [1]

⇒$V' = 8 \pi$ cubic feet

therefore,  the volume of a cone having the same base and same height is, $8 \pi$ cubic feet