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