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The surface area of a showpiece football with volume $38808 c m 3$ will be

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5544 cm 2

8316 cm 2

4158 cm 2

1386 cm 2

answer is A.

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Detailed Solution

We are given a football with volume

38808 cm 3 .

We know that the surface area of a sphere is

4 π r 2

and the volume is

43 π r 3,

where r is the radius of the sphere.
Since it is given that the volume of the sphere is

38808 cm 3,

we can calculate radius of the sphere as,

43 π r 3 = 38808 ⇒ 43 × 227 × r 3 = 38808 ⇒ r 3 = 38808 × 7 × 3 88 ⇒ r 3 = 441 × 21

We can calculated surface area, or the curved surface area of a sphere as,

C S A = 4 π r 2 = 4 × 227 × 21 × 21 = 5544 cm 2

Therefore the surface area of a showpiece football is

5544 cm 2 .

Hence, option (1) is correct.

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