# A right circular cylinder just encloses a sphere of radius r (see Fig. 13.22). Find

i) surface area of the sphere,

ii) curved surface area of the cylinder,

iii) ratio of the areas obtained in (i) and (ii).

**Solution:**

Since the cylinder encloses the sphere as we can see in the figure, the radius of the cylinder will be equal to the radius of the sphere and the height of the cylinder will be equal to the diameter of the sphere.

The radius of the sphere = Radius of the cylinder = r

Height of the cylinder, h = diameter of the sphere = 2r

Thus, h = 2r

The surface area of a sphere with radius r = 4πr^{2}

Curved surface area of a cylinder = 2πrh

(i) Surface area of the sphere = 4πr^{2}

(ii) Curved surface area of the cylinder = 2πrh

= 2πr × 2r [Since, h = 2r]

= 4πr^{2}

(iii) The ratio of the areas obtained in (i) and (ii) is:

4πr^{2}/4πr^{2} = 1/1

Thus, the surface area of the sphere and the curved surface area of the cylinder is 4πr^{2} and the ratio between these areas is 1:1.

**Video Solution:**

## A right circular cylinder just encloses a sphere of radius r. Find i) surface area of the sphere, ii) curved surface area of the cylinder, iii) ratio of the areas obtained in (i) and (ii).

### Class 9 Maths NCERT Solutions - Chapter 13 Exercise 13.4 Question 9:

**Summary:**

It is given that there is a right circular cylinder encloses a sphere of radius r. We have found that the surface area of the sphere is 4πr^{2}, curved surface area of the cylinder is 4πr^{2} and the ratio between their area is 1:1.