Question

The number of spheres of radius 2 cm formed by melting and recasting a sphere of radius 6 cm = .

• A. 27
• B. 36
• C. 64
• D. 16

Answer 1

The correct option is A 27

The volume of a sphere = $\frac{4}{3}$$\times$$\pi$$\times$(radius)${}^3$.
The volume of a sphere of radius 6 cm = $\frac{4}{3}$$\times$$\pi$$\times$(6)${}^3$ cm${}^3$.
The volume of a sphere of radius 2 cm = $\frac{4}{3}$$\times$$\pi$$\times$(2)${}^3$ cm${}^3$.
Hence, the number of cubes formed = $\frac{\frac{4}{3}\times \pi \times (6{)}^{3}c{m}^3}{\frac{4}{3}\times \pi \times (2{)}^{3}c{m}^3}$ = 27.