Question

A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?
A. `V=1/3pir^2h`
B. `V=1/6pir^2`
C. `V=1/12pir^3`
D. `V=2pir^3`

Answer 1

we can use

volume of cone formula

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

where

r' is radius of cone

h' is height of cone

we are given

The radius of the cone is half the radius of the cylinder

so,

$r'=\frac{r}{2}$

The height of the cone is equal to the radius of the cylinder

so,

$h'=r$

now, we can plug values into formula

we get

$V=\frac{1}{3} \pi (\frac{r}{2})^2*r$

we can simplify it

$V=\frac{1}{12} \pi r^3$

so, option-C.........Answer