Question

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

• A. 5 m
• B. 10 m
• C. 2.5 m
• D. 7.5 m

Answer 1

The correct option is C

2.5 m

Given:
Diameter of the well, d = 7 m
$\Rightarrow$ Radius of the well, r = $\frac{7}{2}$ = 3.5 m
Height of the well, h = 20 m
Length of the platform, 1 = 22 m
Breadth of the platform, b = 14 m

Let height of the platform be $h_1.$

Well is in the shape of a cylinder.
Volume of cylinder is given by ${}^{\prime }\pi r^2{h}^{\prime }$.
Platform is in the shape of a cuboid.
Volume of cuboid is given by 'length × breadth × height'.

According to given condition we have:
Volume of the well = Volume of the platform
$\Rightarrow \pi r^{2}h=l\times b\times h_1$

$\Rightarrow \frac{22}{7}\times 3.5\times 3.5\times 20=22\times 14\times h_1$

$\Rightarrow h_1=\frac{\frac{22}{7}\times 3.5\times 3.5\times 20}{22\times 14}$

$\Rightarrow h_1=2.5m$