Question

Please read question and know that the shape is in feet not inches and we are trying to figure out how many cubic yards of soil is needed to fill the bed to a depth of 30in please be as accurate as possible and round up to the nearest yard as needed

Answer 1

First we divide the figure into 3 rectangles and find the volume of each one. This is:

Then, the volume for rectangle 1:

Given, depth of 30 in

$30in\times\frac{1ft}{12in}=2.5ft$

The volume formula is

$V=lwh=15\times5\times2.5=187.5ft^3$

Volume for rectangle 2:

$V=16\times4\times2.5=160ft^3$

Volume rectangle 3 = Volume rectangle 1:

$V=187.5ft^3$

Therefore, the volume of the figure is:

$V=187.5+160+187.5=535ft^3$

Next, we have:

1 yard = 3 ft

So 1 cubic yard is given by

$1yd^3=3\times3\times3=27ft^3$

Hence:

$V=535ft^3\times\frac{1yd^3}{27ft^3}=\frac{535}{27}yd^3=19.81yd^3$

Round up the nearest yard = 20 cubic yard

Answer: 20 cubic yards