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# Choose the Correct Answer of the Following Question: the Surface Areas of Two Spheres Are in the Ratio 16 : 9. the Ratio of Their Volumes is - Mathematics

MCQ

Choose the correct answer of the following question:

The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is

#### Options

• 64 : 27

• 16 : 9

• 4 : 3

• 163 : 93

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#### Solution

Let  the radius of the two spheres be r and R.

As,

"Surface area of the first sphere"/"surface area of the second sphere" = 16/9

=> (4pi"R"^2)/(4pi"r"^2) = 16/9

=> (("R")/"r")^2 = 16/9

=> "R"/"r" = sqrt(16/9)

=> "R"/"r" = 4/3        .........(i)

Now,

The ratio of their volumes= "Volumes of the first sphere"/"Volume of the second sphere"

=((4/3pi"R"^3))/((4/3pi"r"^3))

=> ("R"/"r")^3

=> (4/3)^3

=>"R"/"r" = 4/3            [Using (i)]

= 64/27

= 64 : 27

Hence, the correct answer is option (a).

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