Question : A well of 3 m in diameter is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
Option 1: 4.25 m
Option 2: 2.25 m
Option 3: 1.125 m
Option 4: 1.75 m
Correct Answer: 1.125 m
Solution :
Given: A well of 3 m in diameter is dug 14 m deep.
Here, $h_1=14\ m$, $r_1=\frac{3}{2}\ m,$ and $r_2=4+\frac{3}{2}=\frac{11}{2}\ m$
We know that the volume of the cylinder = $\pi r^2h$
Let the height of the embankment be $h_2\ m$.
According to the question,
$\pi\times (r_1)^2\times h= \pi\times (r_2^2-r_1^2)\times h$
$⇒\pi\times (\frac{3}{2})^2\times 14= \pi\times [(\frac{11}{2}^2)-(\frac{3}{2})^2]\times h$
$⇒\frac{9}{4}\times 14=(\frac{121-9}{4})\times h$
$⇒\frac{9}{4}\times 14= \frac{112}{4}\times h$
$⇒h= \frac{9}{8}$
$⇒h= 1.125$ m
Hence, the correct answer is 1.125 m.
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