Anna Beth has two fish tanks. They are both cubes. The side length of one of the tanks is 15 cm. The side length of the other is 45 cm. What is the ratio of the volume of the smaller tank compared to the volume of the larger tank?

Answer 1

The volume of a cube is found by cubing the length of one side.

Volume of smaller tank: 15 cm × 15 cm × 15 cm = 3,375 cubic cm

Volume of larger tank: 45 cm × 45 cm × 45 cm = 91,125 cubic cm

To find the ratio of the volume of the smaller tank compared to the larger tank, we divide the volume of the smaller tank by the larger tank:

3,375 ÷ 91,125 ≈ 0.037

So the ratio of the volume of the smaller tank compared to the larger tank is approximately 0.037. Alternatively, we could express this ratio as a fraction by simplifying the ratio:

3,375 : 91,125

We can divide both sides by 375 to simplify:

9 : 243

And we can simplify further by dividing both sides by 9:

1 : 27

So the ratio of the volume of the smaller tank compared to the larger tank can be expressed as 1 : 27.

Answer 2

or, in simpler steps ....

ratio of sides = 15:45 = 1:3

The ratio of volumes of similar objects is equal to the cubes of
their corresponding sides, so

ratio of smaller tank : larger tank = 1^3 : 3^3 = 1 : 27

Answer 3

Yes, that's true and a simpler way to approach this problem. Thank you for suggesting it.