# Ex.13.4 Q9 Surface Areas and Volumes Solution - NCERT Maths Class 9

## Question

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).

Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-4 | Question 9

## Text Solution

Reasoning:

The Curved surface area of the cylinder is given by \begin{align} = 2\pi rh \end{align} and Surface area of the sphere\begin{align}\, = 4\pi {r^2} \end{align}

What is known?

Radius of the sphere which touches the cylinder.

(i) Surface area of the sphere

Steps:

Radius of the sphere in $$= r$$

Surface area $$= 4\pi \rm{r^2}$$

(ii) Curved surface area of the cylinder.

Steps:

For cylinder: radius$$=r$$

Height $$=2r$$

Curved surface area of the cylinder

\begin{align}&= 2\pi rh \\&= 2 \times \pi \times r \times 2r \\&= 4\pi {r^2} \end{align}

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

\begin{align} &{\text{Ratio of the area}} \\ &\qquad = \frac{{{\text{Surface area of sphere}}}}{{\left( \begin{array}{l} {\text{Curved surface}} \\ {\text{area of cylinder}} \\ \end{array} \right)}} \\ &\qquad = \frac{{4\pi r^2 }}{{4\pi r^2 }} \\ &\qquad = \frac{1}{1} \\ &\qquad = 1:1 \\ \end{align}

(i) Surface area of the sphere \begin{align} = 4\pi {r^2} \end{align}
(ii) Curved surface area of cylinder \begin{align} = 4\pi {r^2} \end{align}
(iii) Ratio between (i) and (ii) \begin{align} = 1:1 \end{align}