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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?
CBSE | Class 10 | Exercise 16.1 | Maths | RD Sharma | Surface Areas And Volumes
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?

Consider the well to be a solid right circular cylinder

Radius(r) of the cylinder =3.5/2 m=1.75m

Depth of the well or height of the cylinder (h) =16m

As we know that,

Volume of the cylinder \left( {{V}_{1}} \right)=\pi {{r}^{2}}h

=\pi \times {{1.75}^{2}}\times 16

It is given that,

The length of the platform (l) =27.5m

Breadth of the platform (b) =7m

Then, let the height of the platform be x m

We know that,

Volume of the rectangle =l*b*h

{{V}_{2}}=27.5*7*x

As the earth dug up is spread evenly to form the platform

Volumes of both, the well and the platform should be the same.

{{V}_{1}}={{V}_{2}}

\pi \times 1.75\times 1.75\times 16=27.5\times 7\times x

x=0.8m=80cm

Therefore, the height of the platform is 80cm.

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