Question

A cone with a radius of 12 cm and a height of 12 cm has the same volume as a cylinder with a radius of 8 cm. What is the height of the cylinder?
A) 3 cm
B) 6 cm
C) 9 cm
D) 12 cm

Answer 1

Answer:

The correct option is C. The height of the cylinder is 9 cm.

Step-by-step explanation:

The radius of cone is 12 cm and the height of cone is 12 cm.

The volume of cone is

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

$V_1=\frac{1}{3}\pi (12)^2(12)$

$V_1=576\pi$

The radius of cylinder is 8 cm. The volume of cylinder is

$V=\pi r^2h$

$V_2=\pi (8)^2h$

$V_2=64\pi h$

It is given that the volume of cone and cylinder is same.

$V_1=V_2$

$576\pi=64\pi h$

$\frac{576\pi}{64\pi}=h$

$9=h$

Therefore the height of the cylinder is 9 cm and option C is correct.

Answer 2

C 9 becuase of im aswesome and its the correct answer