Question

# Assertion (A) The outer surface of a hemisphere of radius 7 cm is to be painted. The total cost of painting at Rs 5 per cm2 is Rs 2300. Reason (R) The total surface area of a hemisphere is 3π r2. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A). (c) Assertion (A) is true and Reason (R) is false. (d) Assertion (A) is false and Reason (R) is true.

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Solution

## (d) Assertion (A) is false and Reason (R) is true. Assertion (A): Total surface area of the hemisphere$=3\mathrm{\pi }{r}^{2}$ $=\left(3×\frac{22}{7}×7×7\right){\text{cm}}^{2}\phantom{\rule{0ex}{0ex}}=462{\text{cm}}^{2}$ Cost of painting at Rs 5 per cm2$=\text{Rs}\left(462×5\right)$ = Rs 2310 Hence, Assertion (A) is false. Reason (R): The given statement is true.

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