Question

A landscaper has built a U-shaped raised bed in a vegetable garden as shown in the figure. How many cubic yards of soil should be ordered to fill the bed to a depth of 30 inches?

Answer 1

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:

$240in^2\cdot\frac{(1yd)^2}{(36in)^2}=0.185yd^2$

Now, to find the volume convert 30 in to yards:

$30in\cdot\frac{1yd}{36in}=0.83yd$

Finally, multiply the previous result by the area of the figure:

$0.185yd^2\cdot0.83yd=0.154yd^3$