Question

find the ratio of surface area and volume of sphere of unit radius.?

Answer 1

Suppose the radius of the sphere is 'r'.

So. the surface area = 4π r^2
Volume = 4/3 π r^3

Ratio
$4\pi {r}^{2} \div \frac{4}{3}\pi {r}^{3}$
= 4 r^2 / 4/3 r^3
= 1 / 1/3 r
= 3 / r.

So
3 : r is the ratio of the surface area and the volume of the sphere of unit length.

Answer 2

Given:

Radius of sphere = 1 unit

To find:

The ratio of surface area and volume.

Solution:

The formula for the surface area of a sphere = 4πr²- equation 1

The formula for the volume of a sphere = $\frac{4}{3} \pi r^{3}$ - equation 2

On dividing 1 by 2, we get:

= 3/r

On substituting the value of the radius, we get:

The ratio of surface area and volume = 3

Thus, the ratio of surface area and volume will be 3.