Question

two cubes have sides of lengths 7 cm and 3 cm. what is the ratio of their respective volumes? their respective volumes have a ratio of \square: \square. (type a reduced ratio.)

Explanation:

Step1: Recall the formula for the volume of a cube

The volume \(V\) of a cube with side length \(s\) is given by \(V = s^{3}\).

Step2: Calculate the volume of the first cube

For the cube with side length \(s_1=7\) cm, its volume \(V_1 = 7^{3}=7\times7\times7 = 343\) \(cm^{3}\).

Step3: Calculate the volume of the second cube

For the cube with side length \(s_2 = 3\) cm, its volume \(V_2=3^{3}=3\times3\times3=27\) \(cm^{3}\).

Step4: Find the ratio of the volumes

The ratio of the volumes \(V_1:V_2\) is \(\frac{V_1}{V_2}=\frac{343}{27}\).

Answer:

\(343:27\)