The lateral area if a cube varies directly as the square of the edge. If the lateral area is 64 cm and the edge is 4 cm, find the lateral area if the edge is 7 cm.

The lateral area if a cube varies directly as the square of the edge. If the lateral area is 64 cm and the edge is 4 cm, find the lateral area if the edge is 7 cm.

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[tex]\large\sf\underline{Answer:}[/tex]

[tex] \qquad \qquad \huge \rm \: A = 784[/tex]

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[tex]\large\sf\underline{Solution:}[/tex]

The statement, "the lateral area of a cube varies directly as the square of the edge" translated into joint variation is a = ke² where k is the constant of variation.

Solve if lateral area is 64,edge is 4² and edge is 7 So, find the constant using the equation of a combined variation.

[tex]\rm a = ke²[/tex]
[tex]\rm (64) = k(4)²[/tex]
[tex]\rm 64 = 16k[/tex]
[tex]\rm \frac{64}{16} = \frac{16k}{16}[/tex]
[tex]\rm k = 4[/tex]

The constant of the variation is 4. In equation of variation.

[tex]\rm Lateral_{Area} = (4)e²[/tex]

Find lateral area when edgw is 4 and the other edge is 7. Substitute the equation using the constant of the variation that you obtained.

[tex]\rm Lateral_{Area} = ke²[/tex]
[tex]\rm Lateral_{Area} = (4) (7)² [/tex]
[tex]\rm Lateral_{Area} = (4) (49) [/tex]
[tex]\rm Lateral_{Area} = 4(196)[/tex]
[tex]\rm Lateral_{Area} = 784[/tex]

Therefore, the value of the lateral area is 784 when edge is 4 and the other edge is 7.

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