Question

If a solid sphere of radius 20 cm is moulded into 8 solid spherical balls of equal radius, then the radius of each ball will be:

• A. 10 cm
• B. 12 cm
• C. 5 cm
• D. 15 cm

Hint:

When an object is divided into equal parts, volume conservation helps find dimensions of parts using volume formulas.

Answer 1

The Correct Option is A

The volume of the initial large sphere is calculated as: \[V = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (20)^3 = \frac{4}{3} \pi \times 8000 = \frac{32000}{3} \pi\] Let $r$ denote the radius of each of the smaller spheres. The division of the large sphere into 8 equal smaller spheres conserves total volume: \[8 \times \frac{4}{3} \pi r^3 = \frac{32000}{3} \pi\]Dividing both sides by $\frac{4}{3} \pi$ yields: \[8 r^3 = 8000 \implies r^3 = 1000 \implies r = \sqrt[3]{1000} = 10 \text{ cm}\] Therefore, the radius of each smaller sphere is 10 cm.