Question

Emple-12. The hemispherical dome of a building needs to be painted (see lig 1). If the
circumference of the base of dome is 17.6 m, find the cost of painting it given the cost of painting is
Rs5 per 100 cm^2​

Answer 1

${\huge{\sf {\green{\underline{Answer}}}}}$

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Cost = ₹ 985.6

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${\huge{\sf {\green{\underline{Explanation :}}}}}$

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Given :

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• Circumference of the base of a dome = 17.6 m

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• Cost of painting 100 ${cm}^{2}$ = ₹ 5

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To find :

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• Cost of painting the hemispherical dome of the building .

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Solution :

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Area of a circle = π ${r}^{2}$

Area of base = π ${r}^{2}$

↬ $\sf 17.6 = \frac{22}{7} \times r$

↬ $\sf \: (17.6 \times 7) = 22r$

↬ $\sf \: 123.2 = 22r$

↬ $\sf \: r = \frac{123.2}{22}$

↬ $\sf \: r = 5.6 \: cm$

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Curved Surface Area of Hemisphere = 2π ${r}^{2}$

$\sf \: csa = 2 \times \frac{22}{7} \times {(5.6)}^{2}$

⇢ $\sf \: csa = 2 \times \frac{22}{7} \times 31.36$

⇢ $\sf \: csa = \frac{44}{7} \times 31.36$

⇢ $\sf \: csa = 44 \times 4.48$

⇢ $\sf \: csa = 197.12 \: {m}^{2}$

⇢ $\sf \: csa \: = 19712 \: {cm}^{2}$

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Cost of 100 ${cm}^{2}$ = ₹ 5

Cost of 1 ${cm}^{2}$ = ₹ $\frac{5}{100}$

Cost of 19712 ${cm}^{2}$ =

$\frac{5}{100} \times 19712$

= ₹ $\frac{98560}{100}$

= ₹ $985.6$