David is preparing to plant a flower garden with the dimensions as shown in the diagram below. David is going to cover the garden with 3 inches of mulch. Determine how many cubic feet of mulch he...

David is preparing to plant a flower garden with the dimensions as shown in the diagram below. David is going to cover the garden with 3 inches of mulch. Determine how many cubic feet of mulch he needs to buy. Explain your answer.

Diagram:

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The volume is the area of the garden multiplied by the depth of the mulch. We need both area and depth to be in the same units. Since we want cubic feet, convert the depth to feet: 3 inches is `1/4` feet.

To find the area of teh garden we can cut it into two rectangles. One way is to drop a vertical line from the indented corner. Then we have two rectangles:

The small rectangle on the left is a square that is 4ft by 4ft.

The other rectangle is 16ft by 9ft. (The 16ft dimension is given; the 9ft comes from adding the 4ft to the 5ft dimensions.)

The total area is the sum of the areas of the rectangles: Total area = 4x4+16x9=16+144=160 sq ft.

The volume is the area times the depth:

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Volume of mulch required is 160(1/4)=40 cu ft of mulch.

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