Question

A well with 40 m internal diameter is dug 14 m deep. The soil taken out is spread all around to a width of 20 m to form a circular embankment, find the height of the embankment.

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Answer 1

Step-by-step explanation:

given: The diameter of internal well =40 m.

The height of internal well =14 m

The weidth of ciscular embankment =20 m

To find: The height of the embarkment.

$\color{orange} \underline{ \begin{array}{ || |l| || } \hline \color{magenta} \\ \hline \boxed{ \text{ \tt \: Solution:-} } \end{array}}$

$\color{purple} \text{The volume of the well \( \tt=\dfrac{\pi}{4} d_{1}^{2} \times h_{1} \) }$

$\color{red} \text{The volume of embankment \( \tt =\dfrac{\pi}{4} d_{2}^{2} \times h_{2} \)}$

$\color{olive} \[ \begin{array}{l} \tt \Rightarrow \cancel{\dfrac{\pi}{4}} d_{1}^{2} \times h_{1}=\cancel{\dfrac{\pi}{4}} d_{2}^{2} \times h_{2} \\ \\ \tt \Rightarrow(40)^{2} \times 14=(20)^{2} \times h_{2} \\ \\ \tt \Rightarrow h_{2}=\dfrac{(40)^{2} \times 14}{(20)^{2}} \\ \\ \tt \Rightarrow h_{2}=56 \end{array} \]$

Hence, the height of embankment is 56 .