Construction word problem

Question

A water trough is constructed by bending a 4 by 6 foot rectangular sheet of metal down the middle and attaching triangular ends. If the volume of the trough is 9 cubic feet, find the width correct to two decimal places. 

Answer 1

V = LB where B is the area of the base of the solid figure.

 

9 = 6B, so B=1.5.

 

 

The triangular ends are isosceles triangles with equal sides of 2.

 

Triangle area is .5bh where b is the width at the top of the trough and h is the altitude of the triangle.

 

Then 1.5 = .5bh, and bh = 3. Use h = (3/b), and 2 is the hypotenuse of a right triangle that is one-half the triangular end.

 

2² = (b/2)² + (3/b)²

 

4 = (b²/4) + (9/b²)

 

b⁴ - 16b² +36 = 0

 

Applying the Quadratic Formula and taking the square root of the results, we get b ≅ 3.65 or b ≅ 1.65.

 

3.65 checks.

 

h ≅ (3/3.65) ≅ .823   .5(.823)(3.65) ≅ 1.50 for the area of a triangular end. 6(1.50) = 9