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?
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
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.
To find the ratio of the volume of the smaller tank to the larger tank, we need to determine their respective volumes.
The volume of a cube can be found by cubing the length of one side. In this case, the side length of the smaller tank is 15 cm, so its volume is calculated as 15 cm × 15 cm × 15 cm.
Volume of the smaller tank = 15 cm × 15 cm × 15 cm = 3375 cm³
Similarly, the side length of the larger tank is 45 cm, so its volume is:
Volume of the larger tank = 45 cm × 45 cm × 45 cm = 91125 cm³
Now that we have both volumes, we can calculate the ratio by dividing the volume of the smaller tank by the volume of the larger tank:
Ratio of volumes = Volume of smaller tank / Volume of larger tank
= 3375 cm³ / 91125 cm³
Simplifying the ratio, we get:
Ratio of volumes = 1/27
Therefore, the ratio of the volume of the smaller tank to the larger tank is 1:27.