Question

The ratio of the radii of two spheres is :27.(a) Find the ratio of their surface areas.(b) Find the ratio of their volumes.Write these ratios in the format m:n.

Answer 1

Step-by-step explanation:

Recall that surface area is measured in square units while volume is measured in cubic units.

To get the ratio of the surface area and the volume of any solid figure given a scale factor, a:b, all we have to do is get the square and cube of the scale factor.

In the question, the scale factor is 2:7 in which a = 2, and b = 7.

For surface area, square a and b.

`a^2:b^2\Rightarrow2^2:7^2\Rightarrow4:49`

a) Hence, the ratio of the surface area of the smaller sphere to the larger sphere is 4:49.

For the volume, get the cube of a and b.

`a^3:b^3\Rightarrow2^3:7^3\Rightarrow8:343`

b) Hence, the ratio of the volume of the smaller sphere to the larger sphere is 8:343.