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 cm^{2}^{ }is Rs 2300.

Reason (R)

The total surface area of a hemisphere is 3π r^{2}.

(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.

The outer surface of a hemisphere of radius 7 cm is to be painted. The total cost of painting at Rs 5 per cm

Reason (R)

The total surface area of a hemisphere is 3π r

(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$=3\mathrm{\pi}{r}^{2}$

$=\left(3\times \frac{22}{7}\times 7\times 7\right){\text{cm}}^{2}\phantom{\rule{0ex}{0ex}}=462{\text{cm}}^{2}$

Cost of painting at Rs 5 per cm^{2}^{$=\text{Rs}\left(462\times 5\right)$}

= Rs 2310

Hence, Assertion (A) is false.

Reason (R): The given statement is true.

Assertion (A):

Total surface area of the hemisphere$=3\mathrm{\pi}{r}^{2}$

$=\left(3\times \frac{22}{7}\times 7\times 7\right){\text{cm}}^{2}\phantom{\rule{0ex}{0ex}}=462{\text{cm}}^{2}$

Cost of painting at Rs 5 per cm

= Rs 2310

Hence, Assertion (A) is false.

Reason (R): The given statement is true.

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