Question

A 20 m deep well of diameter 7 m. is dug and the earth got by digging is evenly spread out to form a rectangular platform of base 22m × 14m. Find the height of the platform.

Answer 1

Hey dear friend

See attachment ☝☝

Height of platform=2.5m


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Answer 2

Formula used :

$\boxed{\large\mathbf{Volume \: of \: Cylinder = π{r}^{2}h}}$

$\boxed{\large\mathbf{Volume \: of \: Cuboid = lbh}}$

Given,
The well is in the shape of cylinder.
The height of the well is 20m.
The diameter of the well is 7m.

The two dimensions of the rectangular platform (Length and Breadth) are 22m and 14m.
Height of the Rectangular platform = (to be calculated)

$\underline{\underline{\huge\mathfrak{Solution}}}$

We know that,

$\boxed{\boxed{\large\mathbf{Radius = \frac{Diameter}{2}}}}$

Radius of the well = $\frac{7}{2}$

Now, we know that

The earth taken out from the well = The earth spread out in the platform

Hence,

$\boxed{\boxed{\large\mathbf{Volume \: of \: Cuboid = Volume \: of \: Cylinder}}}$

Putting the given values we get,

$22 \times 14 \times h = \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 20 \\ \\ h = \frac{22 \times 7 \times 7 \times 20}{7 \times 2 \times 2 \times 22 \times 14} \\ \\ \bf after \: solving \: we \: get \\ \\ h = \frac{5}{2} \\ \\ \bf h = 2.5m$

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