Question

After doing some work in the house, Bob and Carol want to put a concrete patio on the side of the house to keep people from tracking mud inside. They decide to hire someone to do the work. The dimensions of the rectangular patio are 23 feet 9 inches by 10 feet 1 inch. The patio will need to be at least 4 inches deep. Rachel’s Ready-Mix bid on the job based on the information provided. Make sure that you fill in each answer area before checking "How Did I Do?". Calculate the volume of concrete needed, in cubic yards, adding 5% to allow for spillage and an uneven base Round up to the nearest 14 cubic yard.

Answer 1

Answer:

V=3.098 yd³

Step-by-step explanation:

To answer this question we need to work with formula of the Volume of rectangular prism, the patio. Once it is required 1 inch deep. Some relations will be useful.

As 1 yard = 1 feet/3

1 yard = 1 inch/36

1 feet=12 inches

a) 23 feet 9 inches

23 ft 9''=23 +9/12=23.75 ft

b)10 feet  1 inch

10 feet  1" = 10ft + 1/12=10.083 ft

c)4 inches: 4/12 =0.33

V= w.l.h

V=23.75*10.083*0.33=79.025 ft³

Converting from cubic yard to cubic feet:

V≈79.025 : 27 yd³=2.926 yd³

Considering the possible spillage due to uneven base. ( adding 5%of V)

V≈ 2.92+0.05*(2.92)=3.098 yd³

Answer 2

Answer:

3.25 cubic yard of concrete

Step-by-step explanation:

Additional data:

One cubic yard of concrete 4-inches thick covers 81 square feet.

The dimensions of the rectangular patio are 23 feet 9 inches (23.75 feet) by 10 feet 1 inch (10.083 feet). Then, its area is 23.75 feet*10.083 feet = 239.48 square feet. Using the aforementioned proportion:

1 cubic yard of concrete/x cubic yard of concrete = 81 square feet/239.48 square feet

x = 239.48/81 = 2.96 cubic yard of concrete

Adding 5% to allow for spillage: 2.96*105% = 3.108 cubic yard of concrete

Rounding up to the nearest quarter cubic yard: 3.25 cubic yard of concrete