Question : Aman wants to get his spherical overhead water tank having a diameter of 7 m, painted. If the cost of painting is Rs. 13 per square metre, find the cost of painting Aman's spherical overhead water tank.
(Use $\pi=\frac{22}{7}$)
Option 1: Rs. 1872
Option 2: Rs. 1984
Option 3: Rs. 2002
Option 4: Rs. 1926
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Correct Answer: Rs. 2002
Solution :
The surface area, $A$ of a sphere, where $r$ is the radius of the sphere.
$A = 4\pi r^2$
Given that the diameter $d$ is 7 m
$\therefore r = \frac{7}{2} = 3.5$ m
Substituting $r = 3.5$ m and $\pi = \frac{22}{7}$ into the formula,
$A = 4 \times \frac{22}{7} \times (3.5)^2 = 154 \text{ m}^2$
Given that the cost of painting is Rs. 13 per square metre.
The total cost of painting the tank = 154 × 13 = Rs. 2002
Hence, the correct answer is Rs. 2002.
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