Question

a storage facility is shown below.
in the figure, ( ab = 9 ) feet, ( am = 13 ) feet, ( af = 15 ) feet, and ( cd = 5 ) feet. the storage facility is 12 feet high.
which of the following correctly applies the formulas for finding the volume, ( v ), of the storage facility?
hint: the formula for the area of a trapezoid is ( a=\frac{1}{2}(b_1 + b_2)h ), where ( b_1 ) and ( b_2 ) are the bases, and ( h ) is the height.
3 of 9 questions
( v = 9cdot15cdot13+\frac{1}{2}(12 + 3)(12 - 9)cdot13 )
( v = 9cdot15cdot13+\frac{1}{2}(5 + 15)(9)cdot13 )
( v = 5cdot15cdot13+\frac{1}{2}(5 + 15)(12)cdot9 )
( v = 9cdot15cdot13+\frac{1}{2}(5 + 15)(12 - 9)cdot13 )

Explanation:

Step1: Calculate the volume of the rectangular part

The volume of a rectangular prism is \(V = l\times w\times h\). Here, \(l = AF = 15\) feet, \(w=AB = 9\) feet, and \(h = AM=13\) feet. So the volume of the rectangular part is \(V_{1}=9\times15\times13\).

Step2: Calculate the volume of the trapezoidal - prism part

The formula for the volume of a prism is \(V=A\times h\), where \(A\) is the area of the base. The base is a trapezoid with \(b_1 = CD = 5\) feet, \(b_2=AF = 15\) feet. The height of the trapezoid (in the plane of the trapezoid) is \(12 - 9\) feet (the vertical difference in the height of the two - level structure), and the length (the dimension along which the trapezoid is extruded) is \(AM = 13\) feet.
The area of the trapezoid \(A=\frac{1}{2}(b_1 + b_2)h_{trapezoid}=\frac{1}{2}(5 + 15)(12 - 9)\). Then the volume of the trapezoidal - prism part \(V_{2}=\frac{1}{2}(5 + 15)(12 - 9)\times13\).

Step3: Calculate the total volume

The total volume \(V=V_{1}+V_{2}\), so \(V = 9\times15\times13+\frac{1}{2}(5 + 15)(12 - 9)\times13\)

Answer:

\(V = 9\times15\times13+\frac{1}{2}(5 + 15)(12 - 9)\times13\) (the fourth option)