Question

A cylinder of radius 6 centimetres and height 18 centimetres is melted and recast into spheres of radius 3 centimetres. The number of spheres made from the cylinder is:

• A. 14
• B. 16
• C. 18
• D. 12

Answer 1

Answer:

C. 18

The number of spheres made from the cylinder is 18.

1. Formulae Required

• Volume of a Cylinder = $\pi r^2 h$

• Volume of a Sphere = $\frac{4}{3} \pi R^3$

2. Calculate Cylinder Volume

• Radius ($r$) = $6\text{ cm}$

• Height ($h$) = $18\text{ cm}$

• $\text{Volume} = \pi \times 6^2 \times 18 = 648\pi\text{ cm}^3$

3. Calculate Sphere Volume

• Radius ($R$) = $3\text{ cm}$

• $\text{Volume} = \frac{4}{3} \times \pi \times 3^3 = 36\pi\text{ cm}^3$

4. Find the Number of Spheres

$\text{Number of spheres} = \frac{\text{Volume of Cylinder}}{\text{Volume of Sphere}} = \frac{648\pi}{36\pi} = 18$