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((1yd)^2)/((36in)^2)=0.185yd^2`

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

`30in\cdot(1yd)/(36in)=0.83yd`

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

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