First calculate the area of the shaded region by considering the U-shaped bed as formed by three rectangles, as follow:
where the lengths of the sides of the rectangles corresponds with the dimensions of the U-shaped bed.
Then, for the area of the figure, use the formula for the area of a rectangle, for all three rectangles, as follow:
A = 5*18 + 3*20 + 5*18
A = 90 + 60 + 90
A = 240
Then, the area is 240 in^2
Next, convert the previous result to yd^2. Use the equivalence 1 yd = 36 in:
[tex]240in^2\cdot\frac{(1yd)^2}{(36in)^2}=0.185yd^2[/tex]
Now, to find the volume convert 30 in to yards:
[tex]30in\cdot\frac{1yd}{36in}=0.83yd[/tex]
Finally, multiply the previous result by the area of the figure:
[tex]0.185yd^2\cdot0.83yd=0.154yd^3[/tex]
