Aptitude 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.

**Sudeep Kumar**

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**KARTIK**

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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.

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