Question

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 ?

Answer 1

Radius of the circular pond, $r=\frac{40}{2}=20cm$

Width of the path around the circular pond = 2 m

Outer radius of the circular pond, R = 20 m + 2 m = 22 m

Depth of the gravel path, $h=20cm=\frac{20}{100}=0.2m$

Volume of the gravel path $=\pi (R^2-r^2)h$

$=\frac{22}{7}\times ({22}^2-{20}^2)\times 0.2$

$=\frac{22}{7}\times 84\times 0.2=52.8m^3$

Thus, the volume of the gravel needed in the path is 52.8 m3.