A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 13.10). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

As the capsule is in the shape of a cylinder with 2 hemispheres stuck to its ends, the diameter of the capsule is equal to the diameter of its cylindrical part and the diameter of its hemispherical part.

From Fig. 13.10, it’s clear that the capsule has the curved surface of two hemispheres and the curved surface of a cylinder.

Surface area of the capsule = 2 × CSA of hemispherical part + CSA of cylindrical part

The surface area of the capsule can be found by using formulae;

CSA of the hemisphere = 2πr², where r is the radius of the hemisphere

CSA of the cylinder = 2πrh, where r and h are the radius and height of the Cylinder respectively.

Diameter of the capsule, d = 5 mm

Radius of the hemisphere, r = d/2 = 5/2 mm

Radius of the cylinder, r = 5/2 mm

Length of the cylinder = Length of the capsule - 2 × radius of the hemisphere

h = 14 mm - 2 × 5/2 mm = 9 mm

Surface area of the capsule = 2 × CSA of hemispherical part + CSA of cylindrical part

= 2 × 2πr² + 2πrh

= 2πr (2r + h)

= [2 × 22/7 × 5/2 mm ×  (2 × 5/2 mm + 9 mm)]

= 110/7 mm × 14 mm

= 220 mm²

Thus, the surface area of the capsule is 220 mm².