Geometry & Mensuration

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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.


18 cm


24 cm


36 cm


48 cm

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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 \(h\)


\(=48\text{ cm}\)

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

(3) Comment(s)


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


Why make it complicated?

volume of cone = volume of sphere

As radius is same,on comparing we get

$4 R = H$

$4 x 12 = H = 48 cm$


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