Question

A metallic sphere of radius 8 cm is melted to form a cone with radius same as that of sphere. What is the height of the cone (in cm) ?

• A. 10.7
• B. 12
• C. 16
• D. 32

Answer 1

The Correct Option is D

To find the height of the cone formed by melting a metallic sphere with a radius of 8 cm, follow these steps:

1. Calculate the volume of the sphere using the formula: V_sphere = (4/3)πr³. Here, r = 8 cm. Therefore, V_sphere = (4/3)π(8)³ = (4/3)π(512) = 2048π/3 cm³.
2. Since the metal from the sphere is used to form the cone, their volumes are equal: V_cone = 2048π/3 cm³.
3. Use the formula for the volume of a cone: V_cone = (1/3)πr²h, where r = 8 cm and h is the cone's height we need to find. Substitute the values: (1/3)π(8)²h = 2048π/3.
4. Simplify the equation: (1/3)π(64)h = 2048π/3. This reduces to 64h = 2048.
5. Solve for h by dividing both sides by 64: h = 2048/64 = 32.

The height of the cone is therefore 32 cm.