Question

A cone and cylinder have the same height and the same base radius. If the volume of the cylinder is 81 cm^3 what is the volume of the cone in cm^3?

A) 9
B) 27
C) 78
D)243

Answer 1

Answer:

The volume of the cone is $27cm^3$

Step-by-step explanation:

We know that formulas

Volume of cylinder is

$V_1=\pi r^2 h$

Volume of cone is

$V_2=\frac{1}{3}\pi r^2 h$

we are given

A cone and cylinder have the same height and the same base radius

So, both will have same radius and height

now, we can find ratios

$\frac{V_2}{V_1}=\frac{\frac{1}{3}\pi r^2h }{\pi r^2h}$

now, we can simplify it

$\frac{V_2}{V_1}=\frac{1}{3}$

we are given

the volume of the cylinder is 81 cm^3

so, $V_1=81$

now, we can plug it and solve for V2

$\frac{V_2}{81}=\frac{1}{3}$

$81\times \frac{V_2}{81}=81\times\frac{1}{3}$

$V_2=27$

So, the volume of the cone is $27cm^3$