A conical pit of top diameter 3.5 m is 12m deep. What is its capacity in kilolitres?
Last updated date: 25th Mar 2023
•
Total views: 307.2k
•
Views today: 4.84k
Answer
307.2k+ views
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 \[\pi \].
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
