Question

Find the volume of a trough 5 meters long whose ends are equilateral triangles, each of whose

sides has a length of 2 meters.

Answer 1

`V=5√(3)\ m^3`

Explanation:

we know that

The volume of a trough is equal to

`V=BL`

where

B is the area of equilateral triangle

L is the length of a trough

step 1

Find the area of equilateral triangle B

The area of a equilateral triangle applying the law of sines is equal to

`B=(1)/(2) b^(2) sin(60\°)`

where

`b=2\ m`

`sin(60\°)=(√(3))/(2)`

substitute

`B=(1)/(2)(2)^(2) ((√(3))/(2))`

`B=√(3)\ m^(2)`

step 2

Find the volume of a trough

`V=BL`

we have

`B=√(3)\ m^(2)`

`L=5\ m`

substitute

`V=(√(3))(5)`

`V=5√(3)\ m^3`