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Q.

Find the radius of a sphere whose surface area is 154cm2.

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a

2.5cm

b

3.5cm

c

4.5cm

d

5.5cm

answer is B.

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Detailed Solution

Careful about the area that is given, that is curved surface area or total surface area. Both have different formulas for area.
Total surface area of the sphere is =154cm2 .
Also, the surface area of the sphere is =4πr2 . Where, r is the radius of the sphere.
⇒4πr2=154
Substituting the value of

= \frac{22}{7}

. We get,

\Rightarrow 4 \times \frac{22}{7} \times r^{2} = 154

Divide by 7 on both sides, we get:

\Rightarrow 4 \times 22 \times r^{2} = 154 \times 7

Rearranging the equation for r2.

\Rightarrow r^{2} = \frac{154 \times 7}{22 \times 4}

(Simple multiplication)

\Rightarrow r^{2} = \frac{1078}{88}

\Rightarrow r^{2} = 12.25

Taking square root on both side we get,

\Rightarrow r = \sqrt{12.25}

\Rightarrow r = 3.5

Thus, the radius of the sphere is 3.5 cm

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