Question

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

Options

• 9 : 16

• 16 : 9

• 3 : 4

• 4 : 3

Answer 1

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is 16 : 9.

Explanation:

Let the radii of the spheres be and r.

Then ratio of their volumes

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

Therefore,

`"V"_1/"V"_2 = (4/3pi"R"^3)/(4/3pi"r"^3) = 64/27`

`=> "R"^3/"r"^3 = 64/27`

`=> ("R"/"r")^3 = 64/27`

`=> ("R"/"r")^3 = (4/3)^3`

`= "R"/"r" = 4/3`

Hence, the ratio of their surface areas `= (4pi"R"^2)/(4pi"r"^2)`