Sameer has a solid metal ball having a diameter of 6 cm. He melts it and uses the material for making a solid cylinder. If the diameter of the base of the cylinder is same as that of the ball, what would the height of the cylinder be?

Correct option is B

Formula Used:

Volume of Sphere = $$\frac 43 \pi r^3$$

Volume of Cylinder= $$\pi r^2 h$$​​

Solution:
The diameter of the ball is 6 cm, so the radius r is:
r =$$\frac{6}{2} = 3 \text{ cm}$$​​
The volume V of a sphere is given by:
V =$$\frac{4}{3} \pi r^3$$​​
V = $$\frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi \cdot 27 = 36 \pi \text{ cubic cm}$$​​
The diameter of the base of the cylinder is the same as the diameter of the ball, which is 6 cm. Therefore, the radius r of the cylinder's base is:
r =$$\frac{6}{2} = 3 \text{ cm}$$​​
The volume V of a cylinder is given by:
V = $$\pi r^2 h$$​​
where h is the height of the cylinder.
Since the volume of the melted ball is used to form the cylinder, the volumes are equal:
​$$36 \pi = \pi (3)^2 h$$​​
​$$36 \pi = 9 \pi h$$​​
h = $$\frac{36 \pi}{9 \pi} = 4 \text{ cm}$$​​