Question

If a well of height 20 m and diameter 7 m is dug out and the sand extracted from it is used to make a cuboid platform of length 14 m, breadth 22 m, then what is the height of the platform?

• A. 10 m
• B. 1 m
• C. 2.5 m
• D. 3.5 m

Answer 1

The correct option is C 2.5 m

Given, diameter of well = 7 m
$\therefore$ Radius of well = 3.5 m
Height of the well = 20 m
$\therefore \text{Volume of cylinder}=\pi r^{2}h=\pi \times {3.5}^2\times 20$

Given, cuboid of length = 14 m, breadth = 22 m
Let, height be ${}^{\prime }{h}^{\prime }$ m.
$\therefore \text{Volume of cuboid}=l\times b\times h=14\times 22\times h$

The volume of mud extracted from the well is used to make the platform.
$\therefore$ Volume of platform (cuboid) = volume of well (cylinder)
$\Rightarrow 14\times 22\times h=\pi \times {3.5}^2\times 20\Rightarrow h=2.5m$