Ex.13.7 Q5 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

A conical pit of top diameter \(3.5\rm\, m\) is \(12\rm\, m\) deep. What is its capacity in kiloliters?

Text Solution

Reasoning:

Volume of the cone is \(\begin{align}\frac{1}{3} \end{align}\)times of the volume of a cylinder having radius r and height h \(\begin{align} = \frac{1}{3}\pi {r^2}h \end{align}\).

What is  known?

On a meter and the depth of the cone.

What is  unknown?

Volume in kilometer.

Steps:

Volume of cone \(\begin{align} = \frac{1}{3}\pi {r^2}h \end{align}\)

Height of the cone \((h) =\) depth of the pit.

Height \((h) = 12\rm\, cm\)

Diameter \(= 2r = 3.5\rm\, m\)

\(\begin{align}\therefore r = \frac{{3.5}}{2} \end{align}\)

Volume

\(\begin{align} = \frac{1}{3} \times \frac{{22}}{7} \times {(1.75)^2} \times 12 = 38.5\,\,\rm\,c{m^3} \end{align}\)

\[\begin{align}1\,\,\,\rm\,c{m^3} &= 1000\,\,l = 1\,\,k\,\,l \\\therefore\,\, 38.5\,\,\rm\,c{m^3} &= 38500\,\,l = 38.5\,\,kl \end{align}\]

Answer:

Capacity in kilolitre \(\begin{align} = 38.5\,\,kl \end{align}\).