Question : A sphere of radius 18 cm is melted and then a solid cylinder of base radius 4 cm is made from it. What is the height of the solid cylinder?
Option 1: 196 cm
Option 2: 486 cm
Option 3: 224 cm
Option 4: 384 cm
Correct Answer: 486 cm
Solution :
The volume of the sphere,$V_{\text{s}} = \frac{4}{3}\pi r_{\text{s}}^3$ and the volume of the cylinder is given by the formula $V_{\text{c}} = \pi r_{\text{c}}^2 h_{\text{c}}$ where $r_{\text{s}}$ is the radius of the sphere, $r_{\text{c}}$ is the radius of the base of the cylinder, and $h_{\text{c}}$ is the height of the cylinder.
Since the sphere is melted to form the cylinder, the volumes of the sphere and the cylinder are equal.
$⇒\frac{4}{3}\pi (18)^3 = \pi (4)^2 h_{\text{c}}$
$⇒h_{\text{c}} = \frac{4 \times 18^3}{3 \times 4^2} = 486 \text{ cm}$
Hence, the correct answer is 486 cm.
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