Question

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

Answer 1

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).