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tensa zangetsu [6.8K]
3 years ago
8

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

Mathematics
1 answer:
yawa3891 [41]3 years ago
3 0

Answer:

V=5\sqrt{3}\ m^3

Step-by-step 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=\frac{1}{2} b^{2} sin(60\°)

where

b=2\ m

sin(60\°)=\frac{\sqrt{3}}{2}

substitute

B=\frac{1}{2}(2)^{2} (\frac{\sqrt{3}}{2})

B=\sqrt{3}\ m^{2}

step 2

Find the volume of a trough

V=BL

we have

B=\sqrt{3}\ m^{2}

L=5\ m

substitute

V=(\sqrt{3})(5)

V=5\sqrt{3}\ m^3

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