The side lengths of two different cubes are 36 cm and 45 cm. What is the ratio of the volume of the smaller to the volume of the larger (in simplest form)? Note: These cubes are not drawn to scale.
64/125
65
64/125 trust me i took the test and got it right. :)
To find the ratio of the volume of the smaller cube to the volume of the larger cube, we need to calculate both volumes and then simplify the ratio.
The volume of a cube is given by the formula V = s^3, where 's' represents the length of a side.
Let's calculate the volumes of the two given cubes:
For the smaller cube:
Side length = 36 cm
Volume = (36 cm)^3 = 36 * 36 * 36 = 46656 cm^3
For the larger cube:
Side length = 45 cm
Volume = (45 cm)^3 = 45 * 45 * 45 = 91125 cm^3
Now, we can find the ratio of the two volumes. To simplify the ratio, we need to identify their greatest common divisor (GCD) and divide both volumes by it:
GCD(46656, 91125) = 9
Divide both volumes by the GCD:
Volume of smaller cube / GCD = 46656 cm^3 / 9 = 5184 cm^3
Volume of larger cube / GCD = 91125 cm^3 / 9 = 10125 cm^3
Therefore, the simplified ratio of the volume of the smaller cube to the volume of the larger cube is:
5184 cm^3 : 10125 cm^3
This ratio cannot be further simplified, so 5184 cm^3 : 10125 cm^3 is the final answer.