Question : A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 154 cm, then find the cost of painting it if the cost of painting is INR 4 per 100 cm2. (Use$ ~\pi=\frac{22}{7}$).
Option 1: INR 150.92
Option 2: INR 150.66
Option 3: INR 105.29
Option 4: INR 105.66
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Correct Answer: INR 150.92
Solution :
Let $R$ be the radius.
Circumference of the base of the dome = 154 cm
$⇒2\pi R$ = $154$
$⇒R$ = $\frac{154×7}{2×22}$ = $\frac{49}{2}$ cm
Surface area of hemispherical dome
= $2\pi R^2$
= $2\pi R×R$
= $154×\frac{49}{2}$
= $3773$ cm
2
Cost of painting per 100 cm
2
= INR 4
So, the total cost = $\frac{3773}{100}×4$ = INR 150.92
Hence, the correct answer is INR 150.92.
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