After moving into a new house, a couple wants to have a concrete patio poured to support a hot tub, because....well, because it's a hot tub. The plans call for a 14 ft by 16 ft slab of concrete 4 inches thick. Round any calculations to two decimal places if you need to.

Question

1. How many cubic feet of concrete will be needed? Write 4 inches as .33 ft to compute volume in cubic feet.

2. Convert the volume of concrete to cubic yards.

Answer 1

To find the volume of concrete needed for the patio, we can use the formula for the volume of a rectangular prism:

\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

1. Calculate the volume in cubic feet:

   • Length = 14 ft
   • Width = 16 ft
   • Height = 4 inches, which is converted to feet: \[ 4 \text{ inches} = \frac{4}{12} \text{ feet} = \frac{1}{3} \text{ feet} \approx 0.33 \text{ ft} \]
   • Now plug in the values: \[ \text{Volume} = 14 \text{ ft} \times 16 \text{ ft} \times 0.33 \text{ ft} \] \[ \text{Volume} = 14 \times 16 \times 0.33 = 74.88 \text{ cubic feet} \]

2. Convert the volume from cubic feet to cubic yards:

   • There are 27 cubic feet in one cubic yard.
   • To convert cubic feet to cubic yards, divide the volume in cubic feet by 27: \[ \text{Volume in cubic yards} = \frac{74.88 \text{ cubic feet}}{27} \] \[ \text{Volume in cubic yards} \approx 2.77 \text{ cubic yards} \]

In summary, the couple will need approximately:

1. 74.88 cubic feet of concrete.
2. 2.77 cubic yards of concrete.