Question

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.

Answer 1

Given:

• Circumference of dome = 17.6m
• Cost of painting = Rs.5 per 100cm²

To find:

• Radius.
• Curved surface area of hemispherical dome.
• Total Cost of painting.

Solution:

On using circumference of circle, we have:

Circumference of dome = 2πr

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒17.6 = 2πr

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒17.6 = 2×22/7×r

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒17.6 = 44r/7

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒r = 17.6×7/44

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒r = 2.8m

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒r = 280cm

On applying CSA of hemisphere formula, we have:

C.S.A of Hemispherical dome:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒2πr²

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒2×22/7×280×280

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒2×22×40×280

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$⇒492800cm²

As cost of painting 100cm² is Rs.5, cost of painting 1cm² = Rs.5 × 1/100

•Cost of painting 492800cm² = Rs. 5×492800×1/100

•Cost of painting 492800cm² = Rs. 49280×1/2

•Cost of painting 492800cm² = Rs. 24640

Final Answer:

Cost of painting = Rs. 24640