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Ex.13.7 Q3 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

The height of a cone is \(15\rm\, cm.\) If its volume is \(\begin{align}1570\,\,c{m^3} \end{align}\), find the radius of the base.(Use \(p = 3.14\)).

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-7 | Question 3

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 i.e. \(\begin{align} = \frac{1}{3}\pi {r^2}h \end{align}\)

What is  known?

Volume of the cone and the height of the cone.

What is  unknown?

Radius of the base.

Steps:

Height \((h) = 15\,\rm cm\)

Radius \((r) = ?\)

Volume of cone

\[\begin{align}&= \frac{1}{3}\pi {r^2}h \\1570&= \frac{1}{3}\pi {r^2}h \\ 1570 &= \frac{1}{3} \times 3.14 \times {r^2} \times 15 \\{r^2} &= \frac{{1570 \times 3}}{{15 \times 3.14}} = \frac{{4710}}{{47.1}} \\{r^2} &= 100 \\ r &= \sqrt {100} = 10\,\,\rm\,cm \end{align}\]

Answer:

Radius of the base \(= 10 \rm\,cm\)