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If the volume of a ball is $606.375 m 3,$ then its surface area will be ____ $m 2 .$

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Detailed Solution

If the volume of a ball is

606.375 m 3,

then its surface area will be

346.5 m 2 .

We are given a ball with volume

606.375 m 3 .

We know that the volume of a sphere is

43 π r 3 .

The surface area of a sphere is

4 π r 2,

where r is the sphere’s radius.
Since the volume of the sphere is

606.375 m 3,

therefore we can write,

606.975 m 3 = 43 π r 3 ⇒ 606.375 = 43 × 227 × r 3 ⇒ r 3 = 606.375 × 3 × 7 4 × 22 ⇒ r 3 = 144.703125 m

⇒ r = 5.25 m

Then the surface area of the ball can be calculated as,

S A = 4 π r 2 ⇒ S A = 4 × 227 × 5.25 × 5.25 m 2 ⇒ S A = 346.5 m 2

Therefore, the surface area of the ball is

346.5 m 2 .

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