Anthony is laying concrete for a driveway. The driveway is to be 15 feet long by 12 feet wide by 7 inches deep. Answer parts (a) through (c). (a) Determine the volume of concrete needed in cubic feet. The volume of concrete is \( 105 \mathrm{ft}^{3} \). (Simplify your answer. Type an integer or a decimal.) (b) If 1 cubic yard = 27 cubic feet, how many cubic yards of concrete are needed? (Simplify your answer. Type an integer or a decimal. Round to two decimal places as needed.) (

To solve the problem, we will go through each part step by step. ### Part (a): Determine the volume of concrete needed in cubic feet. The volume \( V \) of a rectangular prism (which is the shape of the driveway) can be calculated using the formula: \[ V = l \times w \times h \] where: - \( l \) is the length, - \( w \) is the width, - \( h \) is the height (or depth). Given: - Length \( l = 15 \) feet, - Width \( w = 12 \) feet, - Depth \( h = 7 \) inches. First, we need to convert the depth from inches to feet. Since there are 12 inches in a foot: \[ h = \frac{7 \text{ inches}}{12 \text{ inches/foot}} = \frac{7}{12} \text{ feet} \] Now we can calculate the volume: \[ V = 15 \times 12 \times \frac{7}{12} \] Calculating this step-by-step: 1. Calculate \( 15 \times 12 = 180 \). 2. Now multiply by \( \frac{7}{12} \): \[ V = 180 \times \frac{7}{12} = 180 \times 0.5833 \approx 105 \text{ cubic feet} \] So, the volume of concrete needed is \( 105 \text{ ft}^3 \). ### Part (b): How many cubic yards of concrete are needed? To convert cubic feet to cubic yards, we use the conversion factor: \[ 1 \text{ cubic yard} = 27 \text{ cubic feet} \] Thus, to find the number of cubic yards \( Y \): \[ Y = \frac{V}{27} \] Substituting the volume we found: \[ Y = \frac{105}{27} \] Calculating this: \[ Y \approx 3.8889 \] Rounding to two decimal places: \[ Y \approx 3.89 \] ### Summary of Answers: (a) The volume of concrete needed is \( 105 \text{ ft}^3 \). (b) The number of cubic yards of concrete needed is approximately \( 3.89 \).