A path 2 m wide surrounds a circular pond of diameter 40 m. How many cubic metres of gravel are required to grave the path to a depth of 20 cm?
Diameter of the circular pond is given = 40 m
So, the radius of this pond is 20 m
There is a path surrounding the pond. We are given the thickness of this path as 2 m
We have to grave this path with gravel. The depth of the path is also given 20 cm=0.2 m
This circular path can be viewed as a hollow cylinder of thickness 0.2 m and depth 0.2 m
We know,
Volume of a hollow cylinder $=\pi h\left(R^{2}-r^{2}\right)$
So the volume of the circular path with height 0.2 m
$=\pi \times 0.2\left(22^{2}-20^{2}\right)$
$=\pi \times 0.2\left(484-400^{2}\right)$
$=\pi \times 0.2 \times 84$
$=52.77 \mathrm{~m}^{3}$
Hence, the volume of gravel required is $52.77 \mathrm{~m}^{3}$