Question

there are two cubes. the first cube has a volume of 1,000 cubic units. the second cube is smaller than the first, with sides only half as long. what is the volume of the second cube? cubic units

Explanation:

Step1: Find side - length of the first cube

The volume formula for a cube is $V = s^3$, where $V$ is volume and $s$ is side - length. Given $V_1=1000$ cubic units, then $s_1=\sqrt[3]{1000}=10$ units.

Step2: Find side - length of the second cube

The second cube has sides half as long as the first. So $s_2=\frac{s_1}{2}=\frac{10}{2} = 5$ units.

Step3: Calculate volume of the second cube

Using the volume formula $V = s^3$, for the second cube with $s = s_2 = 5$ units, we have $V_2=s_2^3=5^3 = 125$ cubic units.

Answer:

125