# Easy Geometry & Mensuration Solved QuestionAptitude Discussion

 Q. A cone and sphere have the same radius of 12 cm. Find the height of the cone if the cone and sphere have the same volume.
 ✖ A. 18 cm ✖ B. 24 cm ✖ C. 36 cm ✔ D. 48 cm

Solution:
Option(D) is correct

Let the height of the cone be $h$

Volume of the cone

$=\dfrac{1}{3}\times \pi \times 12^2\times h$

$=48\pi h\text{ cm}^3$

Volume of the sphere

$=\dfrac{4}{3}\times \pi\times r^3$

$=\dfrac{4}{3}\pi (12)^3$

$=2304\text{ cm}^3$

Since the volumes are equal

$48\pi h=2304\pi$

Solving for $h$

$h=\dfrac{2304\pi}{48\pi}$

$=48\text{ cm}$

Edit: For shortcut and simpler solution check KARTIK's comment.

## (3) Comment(s)

Sudeep Kumar
()

r = 12

volume of cone = 1/3*3.14*r^2*h

volume of sphere = 4/3*3.14*r^3

vol of cone = vol of sphere

4r = h

4(12) = h

h = 48

KARTIK
()

Why make it complicated?

volume of cone = volume of sphere

As radius is same,on comparing we get

$4 R = H$

$4 x 12 = H = 48 cm$

Jeevan
()

Hey Karthik, your shortcut is really cool. Thanks a ton man.