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Ex.13.6 Q1 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

The circumference of the base of a cylindrical vessel is $$132\; cm$$ and its height is $$25\; cm$$. How many litres of water can it hold? \begin{align}(1000\,c{m^3} = 1\,l) \end{align}

Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-6 | Question 1

Text Solution

Reasoning:

Volume of a cylinder of base radius $$r$$ and height is $$V = \pi r^{2} h$$.

What is known?

Circumference of the base and the height.

What is unknown?

Litres of water the cylindrical vessel can hold.

Steps:

Since the base of a cylindrical vessel is a circle, the circumference is $$2 \pi r=132 \mathrm{cm}$$ (given)

\begin{align} 2\pi r &= 132\\2 \times \frac{{22}}{7} \times r &= 132\\r &= \frac{{132 \times 7}}{{2 \times 22}}\\ &= 21\,\,cm \end{align}

Radius \begin{align}(r) = 21\, \rm{cm} \end{align}

Height \begin{align}(h) = 25\, \rm{cm}\end{align}

Capacity of the cylindrical vessel $$=$$ Volume of the cylindrical vessel $$=𝜋𝑟^2ℎ$$

\begin{align}&= \frac{{22}}{7} \times 21 \times 21 \times 25 \\&= 34650\,c{m^3} \end{align}

\begin{align} 1000\,c{m^3} &= 1\,\,l\\34650\,c{m^3} &= x\,\,l\\x &= \frac{{34650}}{{1000}}\\& = 34.65\,l \end{align}
Capacity of the cylindrical vessel\begin{align}= 34.65\,l \end{align}