Question

A well with $10m$ inside diameter is dug $14m$ deep. Earth taken out of it is spread all around to a width of $5m$ to form an embakment, the height of the embankment is ________.

• A. $2.46m$
• B. $3.56m$
• C. $4.66m$
• D. $5.76m$

Answer 1

The correct option is C $4.66m$

Well with $10m$ diameter is dug $14m$ deep.

$\Rightarrow$ Cylindrical radius $=\frac{10}{2}=5m$

Volume $=\pi r^{2}h$

$=\frac{22}{7}\times 5\times 5\times 14$

$=1100$ cubic meter

Is taken out and spread width of $5m.$

( diagram )

$\Rightarrow R_1=5+5=10m$

$r=5m$

$\Rightarrow V=\pi (R^2-r^2)h$

$1100=\frac{22}{7}({10}^2-5^2)h$

$350=(100-25)h$

$h=\frac{350}{75}=\frac{14}{3}$

$\Rightarrow h=4.66m$

Hence, the answer is $4.66m.$