Question

A hemispherical dome of a building needs to be painted from outside. If the circumference of the base of the dome is 17.6 m, find the cost of painting it at the rate of ₹ 2 per 100 cm².

Answer 1

Given:

Circumference of the base of the dome = 17.6 m

Rate of painting = ₹2 per 100 cm²

To Find:

Cost of painting the hemispherical dome from the outside.

Step 1: Find the radius of the dome

Circumference of a circle = 2πr

2πr = 17.6

`2 xx 22/7 xx r = 17.6`

r = `(17.6 xx 7)/44`

r = 2.8 m

Step 2: Find the curved surface area of the hemisphere.

Curved surface area of a hemisphere =2πr²

CSA = `2 xx 22/7 xx (2.8)^2`

= `2 xx 22/7 xx 7.84`

= 49.28 m²

Step 3: Convert area into cm²

1 m² = 10,000 cm²

49.28 m² = 49.28 × 10,000 = 492800 cm²

Step 4: Find the cost of painting

Cost per 100 cm² = ₹2

Cost = `492800/100 xx 2`

= 4928 × 2

= ₹ 9856