Question

The ratio between the volume of two spheres is 8 : 27. What is the ratio between their surface areas?

Options

• 2 : 3

• 4 : 5

• 5 : 6

• 4 : 9

Answer 1

4 : 9
Let the radii of the spheres be R and r, respectively.
Then, ratio of their volumes `= (4/3pi"R"^3)/(4/3pi"r"^3)`

Therefore,

`(4/3pi"R"^3)/(4/3pi"r"^3) = 8/27`

`=> R^3/"r"^3 = 8/27`

`=> ("R"/"r")^3 = (2/3)^3`

`=> R/r = 2/3`

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

`= "R"^2/"r"^2`

`=(2/3)^2`

`= 4/9`

= 4 : 9