Question

the ratio of the side lenghths of two cubes is 3:7. find the ratio of their volumes

Answer 1

27:343 because since the side lengths are like cm or in, it's always to the power of 1, but it is invisible, so since you want to know the ratio of the volume, volume is always inches cubed or centimeters cubed etc. So you get the original ratio of the side lengths to the first power, and do each number to the third power which gives you that ratio.

Answer 2

A ratio shows us the number of times a number contains another number. The ratio of the volume of the cube will be 27:343.

What is a Ratio?

A ratio shows us the number of times a number contains another number.

Let the length of the first cube be 3x, while the length of the second cube is 7x. The volume of a cube is the cube of the length of the side. Therefore, the ratio of the volumes can be written as,

$\dfrac{\text{Volume of first cube}}{\text{Volume of second cube}} = \dfrac{(3x)^3}{(7x)^3}\\\\\\\dfrac{\text{Volume of first cube}}{\text{Volume of second cube}} = \dfrac{27x^3}{343x^3}\\\\\\\dfrac{\text{Volume of first cube}}{\text{Volume of second cube}} = \dfrac{27}{343}$

Hence, the ratio of the volume of the cube will be 27:343.

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