Question

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready.

Answer 1

Given: Height of cylinder h = 20 cm, diameter = 7 cm ⇒ radius r = 3.5 cm.

Step-wise calculation:

1. Total surface area = Curved surface area of cylinder + Curved surface area of two hemispheres

= 2πrh + 2(2πr²)

= 2πr(h + 2r)

2. Substitute r = 3.5 cm and h = 20 cm:

S = 2π(3.5)(20 + 2 × 3.5) 

= 2π × 3.5 × 27 

= 189π cm²

3. Using `π = 22/7` for a numerical value:

`S = 189 xx 22/7` 

= 27 × 22

= 594 cm²