Mathematics: Two cubes have surface areas of 72 square feet and 98 square feet. what is the ratio of the volume of the small cube to the volume of the large cube?

Two cubes have surface areas of 72 square feet and

brandiwingard

13.03.2022

Ratio of the volumes of the cubes = 216 : 343

Step-by-step explanation:

Since surface area of a cube is represented as 6a² where a is the side of a cube.

Let a is one side of large cube and b is the side of smaller one.

Ratio of their surface area = $\frac{6a^{2} }{6b^{2}}=\frac{72}{98}$

$(\frac{a}{b})^{2}=\frac{36}{49}$

$\frac{a}{b}=\sqrt{\frac{36}{49}}$

$\frac{a}{b}=\frac{6}{7}$

Now ratio of the volumes = $\frac{a^{3} }{b^{3}}=(\frac{1}{b})^{3}$

Ratio = $(\frac{6}{7})^{3}=\frac{216}{343}$

Therefore, ratio of the volumes of the cubes = 216 : 343

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anilauferc

02.01.2022

1. No solution (the two lines are parallel)

2. One solution (the two lines intersect at one point)

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