Question

Earth dug out on making a circular tank of radius 7 m is spread all round the tank uniformly to a width of 1 m to form an embankment of height 3.5 m. Calculate the depth of the tank.

• A. $\frac{14}{15}m$
• B. $14$ m
• C. $2$ m
• D. $\frac{15}{14}m$

Answer 1

The correct option is D $\frac{15}{14}m$

Let $h_1$ be the height of circular tank Then
Volume of circular tank= Volume of embankment=$\pi r^2{h}_1$.....(1)
Height of embankment, $h_2$=3.5 m
Inner radius of embankment, $r_1$=7m
Outer radius of embankment, $r_2$=8m
$\therefore$ Volume of embankment=$\pi r_1^2{h}_2-\pi r_2^2{h}_2$
=$\pi (8^2\times 3.5-7^2\times 3.5)$
=$\pi (224-49\times 3.5)=52.5\pi$
Substituting in (1) we get
$\pi \times 7^2\times h_1=52.5\pi$
or $h_1=\frac{52.5}{49}=\frac{7.5}{7}\times \frac{2}{2}=\frac{15}{14}m$