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Question 1 Surface Areas and Volumes - Exercise 13.3

**A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.**

Answer:

t is given that the shape of the well is in the shape of a cylinder with a diameter of 7 m

So, radius = 7/2 m

Also, Depth (h) = 20 m

Volume of the earth dug out will be equal to the volume of the cylinder

∴ Volume of Cylinder = π×r^{2}×h

= 22×7×5 m^{3}

Let the height of the platform = H

Volume of soil from well (cylinder) = Volume of soil used to make such platform

π×r^{2}×h = Area of platform × Height of the platform

We know that the dimension of the platform is = 22×14

So, Area of platform = 22×14 m^{2}

∴ π×r^{2}×h = 22×14×H

22×7×5 m^{3} = 22×14×H

**⇒ H = 2.5 m**

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