Find the volume of a trough 5 meters long whose ends are equilateral triangles, each of whose sides has a length of 2 meters.

Question

asked Dec 21, 2020 136k views

1 Answer

Eithos · Answer 1 · 2020-12-26T17:23:42+0000

Answer:

$V=5√(3)\ m^3$

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)

$V=5√(3)\ m^3$