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.

Question

Calculate the volume of concrete needed, in cubic feet, rounding up to the nearest cubic foot.

 

The delivered cost of the concrete is "$6 per cubic foot plus a $50 surcharge for orders less than 100 cubic feet." Find the total cost having the concrete delivered.

Answer 1

23 feet 9 inches by 10 feet 1 inch and 4 inches deep.

First, put everything into the same units:

23 ft 9 in = 23 9/12 ft = 23 3/4 feet

10 ft 1 in = 10 1/12 feet

4 inches = 4/12 = 1/3 feet

 

Volume = Length*width*height

v = (23 3/4)(10 1/12)(1/3)

= (95/4)(121/12)(1/3)

= 11495/144 ft³

= 79.83 ft³

 

80 ft³

 

Total Cost: 6(80)+50 = $530

Answer 2

9 inches = 9/12 ft = 3/4 ft = 0.75 ft

1 inch = 1/12 ft = 0.083 ft

4 inches = 4/12 ft = 1/3 ft = 0.3 ft

 

The dimensions of patio are 23.75 ft long x 10.083 ft wide x 0.3 ft deep

 

or as fractions      (23 and 3/4) x (10 and 1/12) x (1/3) =

 

                    (95/4)(121/12)(1/3) = 11495/144 = 79 and 119/144 = 79.82638 cubic feet

 

 which agrees with product of the decimal values highlighted in bold above.

 

Rounded to the nearest cubic foot as directed will make the answer 80 cubic feet.

 

The order is less than 100 cubic feet, so there is a surcharge of $50.

 

80 cubic feet x $6 per cubic foot = $480

$480 + $50 = $530