A water trough has two congruent isosceles trapezoids as ends and two congruent rectangles as sides. The exterior surface area of the trough is ________. The volume of the trough is _____. If a trough is emptied until the water level is even with the midsegment of the trapezoidal ends there will be ______ cubic feet of water left in the trough.

Answer:Part a) The exterior surface area is equal to [tex]160\ ft^{2}[/tex]Part b) The volume is equal to [tex]240\ ft^{3}[/tex]Part c) The volume water left in the trough will be [tex]84\ ft^{3}[/tex]Step-by-step explanation:Part a) we know thatThe exterior surface area is equal to the area of both trapezoids plus the area of both rectanglessoFind the area of two rectangles[tex]A=2[12*5]=120\ ft^{2}[/tex]Find the area of two trapezoids[tex]A=2[\frac{1}{2}(8+2)h][/tex]Applying Pythagoras theorem calculate the height h[tex]h^{2}=5^{2}-3^{2}\\h^{2}=16\\h=4\ ft[/tex]substitute the value of h to find the area[tex]A=2[\frac{1}{2}(8+2)(4)]=40\ ft^{2}[/tex]The exterior surface area is equal to[tex]120\ ft^{2}+40\ ft^{2}=160\ ft^{2}[/tex]Part b) Find the volume we know thatThe volume is equal to[tex]V=BL[/tex]whereB is the area of the trapezoidal faceL is the length of the troughwe have[tex]B=20\ ft^{2}\\ L=12\ ft[/tex]substitute[tex]V=20(12)=240\ ft^{3}[/tex]Part c)step 1Calculate the area of the trapezoid for h=2 ft (the half)the length of the midsegment of the trapezoid is (8+2)/2=5 ft[tex]A=\frac{1}{2}(5+2)(2)=7\ ft^{2}[/tex]step 2Find the volumeThe volume is equal to[tex]V=BL[/tex]whereB is the area of the trapezoidal faceL is the length of the troughwe have[tex]B=7\ ft^{2}\\ L=12\ ft[/tex]substitute[tex]V=7(12)=84\ ft^{3}[/tex]