Final answer:
To calculate the amount of topsoil needed, multiply the length by the width of the lawn (50 ft x 80 ft = 4,000 ft²) and then by the thickness (1/3 ft). The resulting volume in cubic feet (1,333.33 ft³) is then converted to cubic yards by dividing by 27, resulting in 49.38 cubic yards of topsoil needed.
Step-by-step explanation:
To calculate the amount of topsoil needed for the lawn, we first need to find the volume in cubic feet and then convert that volume to cubic yards. Starting with the dimensions in feet, the lawn measures 50 feet by 80 feet. We are told that the topsoil needs to be 1/3 foot thick.
First, multiply the length by the width to find the area:
50 ft × 80 ft = 4,000 ft²
Then, multiply the area by the thickness to find the volume:
4,000 ft² × 1/3 ft = 1,333.33 ft³ (repeating)
Finally, to convert cubic feet to cubic yards, we use the conversion that 1 yard is equal to 3 feet. Thus, 1 cubic yard is equal to 3 × 3 × 3 = 27 cubic feet. We divide the total cubic feet (1,333.33) by 27 to find the cubic yards:
1,333.33 ft³ ÷ 27 ft³/yd³ = 49.38 yd³
Therefore, the lawn will require approximately 49.38 cubic yards of topsoil.