Question

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 1

$\huge{\underline{\underline{\sf{\pink{Answer:-}}}}}$

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

So, radius = $\frac{7}{2}$ 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×r²×h

= 22×7×5 m³

Let the height of the platform = H

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

π×r²×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 m²

∴ π×r²×h = 22×14×H

⇒ H = 2.5 m

Answer 2

Answer:

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

∴ Volume of Cylinder = π×r²×h

= 22×7×5 m³

Let the height of the platform = H

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

π×r²×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 m²

∴ π×r²×h = 22×14×H

⇒ H = 2.5 m