# A conical pit of top diameter 3.5 m is 12m deep. What is its capacity in kilolitres?

Last updated date: 25th Mar 2023

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Answer

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Hint: The capacity of the conical pit is equal to the volume of the conical pit. By using the conversion \[1{m^3} = 1{\text{ kilolitre}}\], we can find the capacity of the conical pit. So, use this concept to reach the solution of this problem.

Complete step-by-step answer:

Given,

Height of the conical pit \[h = 12m\]

Diameter of the conical pit \[d = 3.5m\]

So, radius of the conical pit \[r = \dfrac{d}{2} = \dfrac{{3.5}}{2} = 1.75m\]

We know that volume of the conical pit \[V = \dfrac{1}{3}\pi {r^2}h\]

\[

V = \dfrac{1}{3}\pi {\left( {1.75} \right)^2}12 \\

V = \dfrac{1}{3}\pi \left( {3.0625} \right)12 \\

V = \dfrac{1}{3} \times \dfrac{{22}}{7} \times 36.75 \\

V = \dfrac{{22}}{{21}} \times 36.75 \\

V = \dfrac{{808.5}}{{21}} \\

\therefore V = 38.5{\text{ }}{{\text{m}}^3} \\

\]

By using the conversion \[1{m^3} = 1{\text{ kilolitre}}\]

The capacity of the conical pit is 38.5 kilolitres.

Thus, the capacity of conical pit of top diameter of 3.5 m and 12m deep is 38.5 kilolitres.

Note: In the problem we have given the diameter of the conical pit, we have converted it into radius to find the volume of that conical pit. In the solution the value of \[\pi \]is taken as \[\dfrac{{22}}{7}\]. We can also take 3.14 as the value of \[\pi \].

Complete step-by-step answer:

Given,

Height of the conical pit \[h = 12m\]

Diameter of the conical pit \[d = 3.5m\]

So, radius of the conical pit \[r = \dfrac{d}{2} = \dfrac{{3.5}}{2} = 1.75m\]

We know that volume of the conical pit \[V = \dfrac{1}{3}\pi {r^2}h\]

\[

V = \dfrac{1}{3}\pi {\left( {1.75} \right)^2}12 \\

V = \dfrac{1}{3}\pi \left( {3.0625} \right)12 \\

V = \dfrac{1}{3} \times \dfrac{{22}}{7} \times 36.75 \\

V = \dfrac{{22}}{{21}} \times 36.75 \\

V = \dfrac{{808.5}}{{21}} \\

\therefore V = 38.5{\text{ }}{{\text{m}}^3} \\

\]

By using the conversion \[1{m^3} = 1{\text{ kilolitre}}\]

The capacity of the conical pit is 38.5 kilolitres.

Thus, the capacity of conical pit of top diameter of 3.5 m and 12m deep is 38.5 kilolitres.

Note: In the problem we have given the diameter of the conical pit, we have converted it into radius to find the volume of that conical pit. In the solution the value of \[\pi \]is taken as \[\dfrac{{22}}{7}\]. We can also take 3.14 as the value of \[\pi \].

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