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The hemispherical dome of a building needs to be painted. If the circumference of the base of dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs. 5Per $100 {cm}^{2}$

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Rs . 24640

Rs . 25540

Rs . 24440

Rs . 23240

answer is A.

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Detailed Solution

Given,
Circumference of base of dome

C = 17.6 m

So, the radius (r) of the base,

C = 2 πr = 17.6

r = 17.6 \times \frac{7}{2 \times 22} m

r = 2.8 m

C:UserssoftberryDownloadsP0041 JPEGQ.37.jpg

Now the formula for curved surface area of the hemispherical dome

A_{CS} = 2 π r^{2}

Put the values,

A_{CS} = 2 \times \frac{22}{7} \times 2.8 \times 2.8 m^{2}

A_{CS} = 49.28 m^{2}

Painting cost for

100 {cm}^{2}

= Rs. 5
As, 1

m^{2}

= 100000

c m^{2}

Thus,

10000 {cm}^{2} = 1 m^{2}

or,
So,
Painting cost of

1 m^{2} = 5 \times 100 = Rs . 500

Now cost of paint for the dome whose area is 49.28

c m^{2}

= Rs . 500 \times 49.28

= Rs . 24640

Thus, the correct option is 1.

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