Example 7
A hemispherical dome of a building needs to be painted . If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs 5 per 100 cm2.
Since only the rounded surface of the dome is to be painted,
we would need to find the curved surface area of the hemisphere
Let radius of dome be r
Circumference of dome = Circumference of circle with radius r
17.6 = 2πr
17.6 = 2 × 22/7 × r
17.6 × 7/(2 × 22) = r
r = 17.6 × 7/(2 × 22) m
r = 2.8 m
r = 2.8 × 100 cm
r = 280 cm
The curved surface area of the dome = 2πr2
= 2 ×22/7 × (280) × (280) cm2
= 2 × 22 × (40) × (280) cm2
= 492800 cm2
Now, cost of painting 100 cm2 = Rs 5.
Cost of painting 1 cm2 = Rs 5 × 1/100
Cost of painting 492800 cm2 = Rs 5 × 1/100 × 492800
= Rs 24640
Cost of painting the dome is Rs 24,640

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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