Questions & Answers

Question

Answers

$

A.{\text{ 2}}{\text{.46 m}} \\

{\text{B}}{\text{. 3}}{\text{.56 m}} \\

{\text{C}}{\text{.}}{\text{ 4}}{\text{.66 m}} \\

{\text{D}}{\text{. 5}}{\text{.75 m}} \\

$

Answer
Verified

Here, we will Use$V = \pi {r^2}h$, and $V = \pi ({R^2} - {r^2})h$

$

D = 10\;m \\

\therefore r = \dfrac{d}{2} \\

\therefore r = \dfrac{{10}}{2} \\

\therefore r = 5m \\

$

Depth, $h = 14m$

$

V = \pi {r^2}h \\

V = \dfrac{{22}}{7} \times 5 \times 5 \times 14 \\

$

Simplify the above equation –

$V = 1100{m^3}$

The spread all around the well of the width of $5m$ to form an embankment –

Therefore, new radius,

$

R = 5 + 5 \\

R = 10m \\

$

$

V = \pi ({R^2} - {r^2})h \\

V = \dfrac{{22}}{7} \times ({10^2} - {5^2}) \times h \\

$

Substitute, $V = 1100{m^3}$in the above equation.

$1100 = \dfrac{{22}}{7} \times (100 - 25) \times h$

Simplify the above equation – Denominator gets multiplied when it changes the side

$1100 \times 7 = 22 \times 75 \times h$

Make unknown “h” as the subject and simplify the equation-

$

h = \dfrac{{1100 \times 7}}{{22 \times 75}} \\

h = 4.66m \\

$

Thus, the required solution is the height of the embankment is $h = 4.66m$

Hence, from the given multiple choices, the option C is the correct answer.