Question

A medicine capsule is in the form of a cylinder with two hemispheres joined together at the ends. Find the surface area if the length of the capsule is 14 mm and the width is 5 mm.

(a) 219.8 mm^2

(b) 105 mm^2

(c) 115.4 mm^2

(d) 317.2 mm^2

This question was posed to me in final exam.

My doubt is from Surface Area and Volume of Combination of Solids in division Surface Area and Volumes of Mathematics – Class 10

Answer 1

Right choice is (a) 219.8 mm^2

To explain: Radius of the common base (r) = 2.5 mm because the width of the capsule is equal to the diameter of the cylinder.

Length of the cylinder (h) = length of the capsule – 2(radius of the hemisphere) = 14 – 2(2.5) = 9 mm

The surface area of the capsule = C.S.A of the cylinder + 2(C.S.A of the hemisphere)

= 2πrh + 2(2πr^2)

= (2 × 3.14 × 2.5 × 9) + 2(2 × 3.14 × 2.5^2)

= 219.8 mm^2