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Equations for Area and Volume - Algebra

by Sha
(Atlanta, GA)










































v=b3-6b2=9b

1.find an expression for the length of each side of the square bottom by factoring the expression on the right side of the function.

2. use the function to find the volume of a cage with a height of 18 inches.

3. use the accompanying graph to estimate the height of a cage for which the volume is 20,000 cubic inches.

Comments for Equations for Area and Volume - Algebra

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Mar 15, 2012
Equations for Area and Volume
by: Staff


Question:

by Sha
(Atlanta, GA)

v=b3-6b2=9b

1.find an expression for the length of each side of the square bottom by factoring the expression on the right side of the function.

2. use the function to find the volume of a cage with a height of 18 inches.

3. use the accompanying graph to estimate the height of a cage for which the volume is 20,000 cubic inches.



Answer:

Volume of a bird cage.

A company makes rectangular shaped bird cages with height b inches and square bottoms. The volume of these cages is given by the function

V = b³ - 6b² + 9b


a) Find an expression for the length of each side of the square bottom by factoring the expression on the rightside of the function.

V = b³ - 6b² + 9b

V = b * (b² - 6b + 9)

V = b * (b - 3)²

>>> length of each side of the square bottom = b - 3



b) Use the function to find the volume of a cage with a height of 18 inches.

V = b³ - 6b² + 9b

V = 18³ - 6*18² + 9*18

V = 5832 - 6*324 + 162

V = 5832 - 1944 + 162

>>> V = 4050 in³


c) Use the accompanying graph to estimate the height of a cage for which the volume is 20,000 in³.


To view the graph, open the following link.


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http://www.solving-math-problems.com/images/graph-volume-bird-cage-2012-03-15-02.png


>>> For a volume of 20,000 in³, the height of the cage will be 30 inches.




Thanks for writing.

Staff
www.solving-math-problems.com



Jul 14, 2012
Rectangualr shaped bird cage
by: Nadine Johnson

A company makes rectangular shaped bird cages with height b inches and square bottoms. The volume of these cages is given by the function

Find an expression for the length of each side of the square bottom by factoring the expression on the right side of the function.
Use the function to find the volume of a cage with a height of 18 inches.
Use the accompanying graph to estimate the height of a cage for which the volume is 20,000 cubic inches.

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