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word problems - volume

by dena











































using the 5 steps.
The volume of a rectangular slab of concrete needs to exceed 72 cu. in. If teh length is 12 feet and the width is 8 feet, how thick does the concrete slab need to be?

Comments for word problems - volume

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Mar 31, 2011
Word Problems - Volume
by: Staff


The question:

by Dena


using the 5 steps.
The volume of a rectangular slab of concrete needs to exceed 72 cu. in. If teh length is 12 feet and the width is 8 feet, how thick does the concrete slab need to be?


The answer:

I think the 72 cu in the problem statement is a typo. If cubic inches is used for volume, the thickness of the slab would only be around 5/1000 inches thick.

Since the length and width are given in feet, I’m going to assume the 72 cu in should be 72 cu ft.

That assumption made, the answer to your question can be determined as follows:


V = volume of slab in cubic feet

L = length of slab in inches = 12 feet

W = width of slab in inches = 8 feet

T = thickness of the slab in feet


Step 1. The formula for the volume of the slab is:

V = L * W * T

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

V > 72


Step 2. Substitute 72 for V

V = L * W * T > 72

L * W * T > 72


Step 3. Solve for T by dividing each side of the inequality by L*W

L * W * T > 72

(L * W * T )/(L * W) > 72/(L * W)

T *( L * W)/(L * W) > 72/(L * W)

T * 1 > 72/(L * W)

T > 72/(L * W)

In other words, the thickness of the slab, in cubic feet, must be greater than 72 ft³ divided by (Length times Width).


Step 4. The next step is to substitute known values into the inequality:

T > 72/(L * W)

T > 72/(12 * 8)

T > 0.75 feet


Step 5. Convert the thickness to inches

0.75 feet * 12 inches per foot = 9 inches


The final answer is: the thickness of the slab must be greater than 9 inches.



Thanks for writing.


Staff
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