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 first cube

Let the side - length of the first cube be $a$. The volume formula of a cube is $V = a^{3}$. Given $V_1=a^{3}=1000$, then $a=\sqrt[3]{1000}=10$.

Step2: Find side - length of second cube

The side - length of the second cube, $b$, is half of the side - length of the first cube. So $b=\frac{a}{2}=\frac{10}{2} = 5$.

Step3: Calculate volume of second cube

Using the volume formula $V = b^{3}$, substitute $b = 5$ into it. Then $V_2=b^{3}=5^{3}=125$.

Answer:

125