Question

rachel wants to put mulch around her three raised flower beds, as shown in the figure below. each of the three rectangular beds is 3 feet in width and 4 feet in length. rachel needs to fill the 13 foot by 6 foot rectangular area around the beds with mulch to a depth of 3 inches. what volume of mulch does rachel need to buy? a. 10.5 cubic feet b. 19.5 cubic feet c. 42 cubic feet d. 126 cubic feet

Explanation:

Step1: Convert depth to feet

Since 1 foot = 12 inches, 3 inches = $\frac{3}{12}=0.25$ feet.

Step2: Calculate the area to be filled

The area of the large rectangle is $A_{total}=13\times6 = 78$ square - feet.
The area of each small flower - bed is $A_{bed}=3\times4 = 12$ square - feet.
The total area of the 3 flower - beds is $A_{beds}=3\times12 = 36$ square - feet.
The area to be filled with mulch is $A = A_{total}-A_{beds}=78 - 36=42$ square - feet.

Step3: Calculate the volume of mulch

The volume $V$ of mulch is given by the formula $V = A\times h$, where $A$ is the area to be filled and $h$ is the depth.
Substitute $A = 42$ square - feet and $h = 0.25$ feet into the formula: $V=42\times0.25 = 10.5$ cubic - feet.

Answer:

A. 10.5 cubic feet