logo for solving-math-problems.com
leftimage for solving-math-problems.com

help - solve dimension problem

by Jen
(utah)











































A concrete slab will have the following shape and dimensions:

   • Shape: rectangular prism

   • Length: 12 feet

   • Width: 8 feet

   • Volume: needs to be greater than 72 ft³

Calculate how thick the concrete slab must be to satisfy these specifications.

Comments for help - solve dimension problem

Click here to add your own comments

Feb 09, 2011
Calculate Thickness of Concrete Slab
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:


Click the link below to see a 3-D drawing of your problem:

http://www.solving-math-problems.com/images/calculate-volume-concrete-slab.png


The volume of the slab can be calculated as follows:

Volume of Concrete Slab = Length x Width x Thickness

These are the known values

Volume > 72 cubit feet (volume must be greater than 72 cubic feet)

Length = 12 feet

Width = 8 feet

Thickness = unknown

Substituting the known values into the equation

Volume of Concrete Slab = Length x Width x Thickness

Volume of Concrete Slab = Length x Width x Thickness > 72 cubic feet

Length x Width x Thickness > 72 cubic feet

(12 feet) x (8 feet) x Thickness > 72 cubic feet

The last step is to solve for the Thickness. Note that the answer will be in feet.

(12 feet) x (8 feet) x Thickness > 72 cubic feet

(96 square feet) x Thickness > 72 cubic feet

Divide each side of the equation by 96 square feet

(96 square feet) x Thickness > 72 cubic feet

(96 square feet) x Thickness/(96 square feet) > (72 cubic feet)/(96 square feet)

[(96 square feet)/(96 square feet)] x Thickness > (72 cubic feet)/(96 square feet)

(1) x Thickness > (72 cubic feet)/(96 square feet)

Thickness > (72 cubic feet)/(96 square feet)

Thickness > (72/96) x (ft x ft x ft)/(ft x ft)

[note: ft x ft x ft = cubic feet, ft x ft = square feet]

Thickness > (72/96) x (ft x ft)/(ft x ft) x ft

Thickness > (72/96) x (1) x ft

Thickness > (72/96) x ft

Thickness > 0.75 ft

The final answer: the Thickness must be greater than 0.75 feet (or, greater than 9 inches)




Thanks for writing.


Staff
www.solving-math-problems.com


Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com