Questions: Use the plot plan shown in the figure and give your answers to the nearest cubic yard. (a) How many cubic yards of sawdust are needed for preparation of the lawn area if it is to be spread to a depth of three inches? (b) How many cubic yards of gravel are necessary for the walkway if it is to be placed to a depth of two inches? (c) How much compost is available if the pit is eight inches deep? (d) Suppose that you wish to pave the driveway. How much concrete is needed if it is to be poured to a depth of three inches?

Solution Steps

The dimensions of the lawn are given as 35 feet by 15 feet. To find the area: \[ \text{Area} = 35 \, \text{ft} \times 15 \, \text{ft} = 525 \, \text{ft}^2 \]

The depth of sawdust is given as 3 inches. Convert this to feet: \[ 3 \, \text{inches} = \frac{3}{12} \, \text{feet} = 0.25 \, \text{feet} \]

Multiply the area by the depth to find the volume in cubic feet: \[ \text{Volume} = 525 \, \text{ft}^2 \times 0.25 \, \text{ft} = 131.25 \, \text{ft}^3 \]

There are 27 cubic feet in a cubic yard. Convert the volume to cubic yards: \[ \text{Volume} = \frac{131.25 \, \text{ft}^3}{27} = 4.86 \, \text{yd}^3 \]

Final Answer