A $16m$ deep well with diameter $3.5m$ is dug up and the earth from it is spread evenly to form a platform $27.5m$ by $7m$. Find the height of the platform.
Last updated date: 19th Mar 2023
•
Total views: 307.8k
•
Views today: 5.88k
Answer
307.8k+ views
Hint: - Volume of earth will be always constant. That’s why the volume of wells will equal the volume of the platform. So when you compare both volumes you can find the height of the platform.
Volume of earth that has been dug out will be equal to the volume of the well.
Volume of well =$\pi {r^2}h$
Where radius is $\frac{{3.5}}{2}m$ and height is $16m$
That is volume of earth = $\pi \times \frac{{3.5}}{2} \times \frac{{3.5}}{2} \times 16$=$153.86{m^3}$
The earth which has been dug out has to be used to make the platform.
So, volume of platform=volume of earth
Platform is in the shape of cuboid so we use
Volume of cuboid ${\text{L}} \times {\text{B}} \times {\text{H}}$
$ \Rightarrow 27.5m \times 7m \times H = 153.86{m^3}$
$ \Rightarrow H = 0.799m$
Hence, height of the platform is $0.799m$
Note: -First you have to find how much volume of earth is taken out and compare that volume with the volume of platform .Volume of platform will be the same as volume of cuboid ,Because platform is in the shape of cuboid.
Volume of earth that has been dug out will be equal to the volume of the well.
Volume of well =$\pi {r^2}h$
Where radius is $\frac{{3.5}}{2}m$ and height is $16m$
That is volume of earth = $\pi \times \frac{{3.5}}{2} \times \frac{{3.5}}{2} \times 16$=$153.86{m^3}$
The earth which has been dug out has to be used to make the platform.
So, volume of platform=volume of earth
Platform is in the shape of cuboid so we use
Volume of cuboid ${\text{L}} \times {\text{B}} \times {\text{H}}$
$ \Rightarrow 27.5m \times 7m \times H = 153.86{m^3}$
$ \Rightarrow H = 0.799m$
Hence, height of the platform is $0.799m$
Note: -First you have to find how much volume of earth is taken out and compare that volume with the volume of platform .Volume of platform will be the same as volume of cuboid ,Because platform is in the shape of cuboid.
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
