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volume of a rectangular slab of concrete











































The volume of a rectangular slab of concrete needs to exceed 72 cu. ft. If the length is 12 feet and the width is 8 feet, how thick does the concrete slab need to be?

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Dec 08, 2010
Word Problem - Inequality
by: Staff

The question:



The volume of a rectangular slab of concrete needs to exceed 72 cu. ft.

If the length is 12 feet and the width is 8 feet, how thick does the concrete slab need to be?


The answer:

I’m going to use the following variables:

V = volume of slab in cubic feet

L = length of slab in feet

W = width of slab in feet

T = thickness of the slab in feet


The concrete slab is a rectangular solid (a Cuboid). The formula for the volume of the slab is:

V = L x W x T

The volume of the concrete slab in your problem must be greater than 72 cubic feet:

V > 72

The known measurements are:

L = 12

W = 8


With this information, we can now solve for the thickness of the slab:

Begin with what is known about the volume

V = L x W x T

V > 72

Substitute the L x W x T for the V

L x W x T > 72

Substitute the values of the known variables

12 x 8 x T > 72


Solve for T

12 x 8 x T > 72

96 x T > 72

(96 x T)/96 > 72/96

(96/96) x T > 72/96

1 x T > 3/4

T > 3/4

The final answer is: the thickness of the slab must be greater than ¾ ft (greater than 9 inches)


Thanks for writing.


Staff
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