Class nine Mathematics Chapter 13 NCERT Solutions

Chapter 13: Surface Areas and Volumes

8. A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

Sol. Inner radius of the bowl (r) = 5 cm

Thickness of the steel = 0.25 cm

∴ Outer radius of the bowl (R)

= (5 + 0.25) cm = 5.25 cm

Outer curved surface area of the bowl = 2πR²

= 2 × 22/7 × (5.25)² cm² = 173.25 cm²

9. A right circular cylinder just encloses a sphere of radius r (see figure). Find

(i) surface area of the sphere,

(ii) curved surface area of the cylinder, (iii) ratio of the areas obtained in (i) and (ii).

Sol. Here, radius of the sphere = r

Radius of the cylinder = r

And, height of the cylinder = 2r

(i) Surface area of the sphere = 4πr²

(ii) Curved surface area of the cylinder

= 2πrh = 2π × r × 2r = 4πr²

(iii) Required ratio