Question

A hexagonal hole with each side 2m is dug in a school ground to collect rain water. It is 5m deep. Currently it has water, 1 m deep. How much water is collected in the hole?

• A. $6\sqrt{3}{m}^3$
• B. $6m^3$
• C. $5\sqrt{3}{m}^3$
• D. $4\sqrt{3}{m}^3$

Answer 1

The correct option is A

$6\sqrt{3}{m}^3$

Length of each side of the regular hexagon = 2m

The area of one triangular base = $\frac{\sqrt{3}}{4}\times (2{)}^2=\sqrt{3}{m}^2$

The area of the hexagon formed by six of these

=$6\times \sqrt{3}$

=$6\sqrt{3}{m}^2$

Height of the water in it = 1m

Volume of water in it = Area of the base $\times$ height

= $6\sqrt{3}\times 1$

=$6\sqrt{3}{m}^3$