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# Ex.13.6 Q4 Surface Areas and Volumes Solution - NCERT Maths Class 9

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## Question

If the lateral surface of a cylinder is  $$92.4\,\,\rm cm^2$$ and its height is $$5\; \rm cm$$, then find

(ii) its volume. (Use $$\pi = 3.14$$)

Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-6 | Question 4

## Text Solution

Reasoning:

Lateral surface area of a cylinder is $$2\pi rh$$.

Volume of cylinder is $$\pi {r^2}h.$$

What is known?

Lateral surface area of the cylinder and its height.

What is unknown?

Steps:

Lateral surface area of a cylinder having $$r$$ as radius and height $$h$$ is $$2\pi rh$$

Lateral surface area  $$= 94.2\, \rm cm^2$$

$$\text{Height}\; h = 5\; \rm cm$$

\begin{align}2\pi rh &= 94.2\\2 \times 3.14 \times r \times 5 &= 94.2\\r &= \frac{{94.2}}{{5 \times 3.14 \times 2}} \\ & = 3\,\,\rm cm \end{align}

What is unknown?

Volume of the cylinder.

Steps:

$$\text{Radius}\; r = 3\; \rm cm$$

$$\text{Height}\; h = 5\; \rm cm$$

Volume of cylinder

\begin{align} & =\pi r^{2} h \\ & =3.14 \times 3 \times 3 \times 5 \\ & =141.3 \, \mathrm{cm}^{3}\end{align}

$$\text{Radius of its base} = 3\; \rm cm$$
Its volume $$= 141.3\,\, \rm cm^3$$