Question

Find the surface areas and volumes of spheres of the following radii.

(i) 4 cm (ii) 9 cm (iii) 3.5 cm. ( $\mathrm{\pi }=3.14$)

Answer 1

(i)
Radius of the sphere, r = 4 cm

Surface area of the sphere = 4$\mathrm{\pi }$r² = 4 × 3.14 × (4 cm)² = 200.96 cm²

Volume of the sphere = $\frac{4}{3}\mathrm{\pi }{r}^3=\frac{4}{3}\times 3.14\times {\left(4\mathrm{cm}\right)}^3$ = 267.95 cm³

(ii)
Radius of the sphere, r = 9 cm

Surface area of the sphere = 4$\mathrm{\pi }$r² = 4 × 3.14 × (9 cm)² = 1017.36 cm²

Volume of the sphere = $\frac{4}{3}\mathrm{\pi }{r}^3=\frac{4}{3}\times 3.14\times {\left(9\mathrm{cm}\right)}^3$ = 3052.08 cm³

(iii)
Radius of the sphere, r = 3.5 cm

Surface area of the sphere = 4$\mathrm{\pi }$r² = 4 × 3.14 × (3.5 cm)² = 153.86 cm²

Volume of the sphere = $\frac{4}{3}\mathrm{\pi }{r}^3=\frac{4}{3}\times 3.14\times {\left(3.5\mathrm{cm}\right)}^3$ = 179.50 cm³