A path $ 2 \mathrm{~m} $ wide surrounds a circular pond of diameter $ 40 \mathrm{~m} $. How many cubic metres of gravel are required to grave the path to a depth of $ 20 \mathrm{~cm} $?

Given:

A path \( 2 \mathrm{~m} \) wide surrounds a circular pond of diameter \( 40 \mathrm{~m} \).

To do:

We have to find the amount of gravel required to grave the path to a depth of \( 20 \mathrm{~cm} \).

Solution:

Diameter of the pond $= 40\ m$

This implies,

Radius of the pond $r =\frac{40}{2}$

$=20\ m$
Width of the path $= 2\ m$

This implies,

Outer radius $\mathrm{R})=20+2$

$=22 \mathrm{~m}$

Area of the path $=\pi \mathrm{R}^{2}-\pi r^{2}$

$=\pi(22^{2}-20^{2})$

$=\frac{22}{7}(484-400)$

$=\frac{22 \times 84}{7}$

$=264 \mathrm{~m}^{2}$

Height of the gravel used $=20 \mathrm{~cm}$

$=\frac{20}{100}$

$=\frac{1}{5} \mathrm{~m}$

Volume of the gravel used on the path $=$ Area $\times$ Height

$=264 \times \frac{1}{5}$

$=52.8 \mathrm{~m}^{3}$

$52.8$ cubic metres of gravel is required to grave the path to a depth of \( 20 \mathrm{~cm} \).

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Updated on: 10-Oct-2022

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