Volume is a three-dimensional scalar quantity. The cost Ralph needs to spend on concrete for the job to be done is $187.
The amount of three-dimensional space enclosed by a closed surface is expressed as a scalar quantity called volume.
The volume of the concrete that will be needed for the slab with a length of 12 feet, a width of 9 feet, and a thickness of 6 inches(1/2 feet). can be written as
[tex]\rm \text{Volume of Concrete} = Length \times Width \times Thickness[/tex]
[tex]\rm = 12 \times 9 \times \dfrac12\\\\=54\ ft^3[/tex]
As it is given that 10% extra concrete is needed for the spillage. Therefore, the volume of concrete that will be needed is,
[tex]\rm Concrete\ Needed= 54 (100\%+10\%) = 54(110\%) = 59.4\ ft^3[/tex]
Now the volume of the concrete in yds³ can be written as,
[tex]\rm Concrete\ Needed= 59.4\ ft^3 = \dfrac{59.4}{27} = 2.2\ yds^3[/tex]
As it is known that the cost of concrete is $85 per cubic yard, therefore, the cost of the concrete can be written as,
[tex]\rm Total\ Cost = (Concrete\ Needed) \times \text{(Cost per cubic yard)}[/tex]
[tex]=2.2 \times \$85\\\\= \$187[/tex]
Thus, the cost Ralph needs to spend on concrete for the job to be done is $187.
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