FURNITURE A modern table is constructed with four legs made
of concrete cubes with cube-shaped notches.
a. Define one or more variables and write an expression that
represents the volume of one table leg.

b. Marisol determined that she will use 12,636 cubic inches of
concrete to construct the four table legs. If the sides of the
notches are 40% of the sides of the legs, how long are the sides of the legs?

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MrRoyal MrRoyal · Answer 1 · 2021-12-20T15:06:47+01:00

The volume of a shape is the amount of space in it.

The expression that represents the volume of one table leg is: [tex]V = l^3 + n^3[/tex]
The sides of the legs is 14.37 inches long

(a) The volume of one table leg

Represent the side length of the leg with l, and the side length of the notch with n.

So, the expression that represents the volume of one table leg is:

[tex]V = l^3 + n^3[/tex]

(b) The length of the sides

From the question, we have:

[tex]n = 40\% \times l[/tex]

Express 40% as decimal

[tex]n = 0.40 \times l[/tex]

[tex]n = 0.4l[/tex]

Substitute 0.4l for n in [tex]V = l^3 + n^3[/tex]

[tex]V =l^3 + (0.4l)^3[/tex]

[tex]V =l^3 + 0.064l^3[/tex]

[tex]V =1.064l^3[/tex]

The volume of the 4 legs is given as: 12636

So, the volume of one leg would be 12636/4

So, we have:

[tex]1.064l^3 = \frac{12636}{4}[/tex]

[tex]1.064l^3 = 3159[/tex]

Divide both sides by 1.064

[tex]l^3 = 2968.985[/tex]

Take cube roots of both sides

[tex]l = 14.37[/tex]

Hence, the sides of the legs is 14.37 inches long