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MCQ

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

#### Options

1 : 2

2 : 3

9 : 16

16 : 9

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#### Solution

Ist sphere

`V_1 = 4/3 pir_1^2`…… (*i*)

IInd sphere

`V_2 = 4/3 pir_2^3`…… (*ii*)

Divide (*i*) by (*ii*) we get,

`V_1/V_2 = (4/3pi r_1^3)/(4/3pi r_2^3)`

`64/27 = (r_1/r_2)^3`

`r_1/r_2 = sqrt(64/27)`

`r_1/r_2 = 4/3`

Now, the ratio of their C.S.A

`S_1/S_2 = (4pir_1^2)/(4pir_2^2)= (r_1/r_2)^2`

`S_1/S_2 = (4/3)^2 = 16/9`

Hence, `S_1 :S_2 = 16 :9`

Is there an error in this question or solution?