Question

the volume of a cube is 343 cm³. find the length of its side.

Explanation:

Step1: Recall the volume formula for a cube

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

Step2: Substitute the given volume into the formula

We know that \( V = 343 \, \text{cm}^3 \), so we have the equation \( s^3 = 343 \).

Step3: Solve for \( s \)

To find \( s \), we take the cube root of both sides of the equation. The cube root of 343 is 7 because \( 7 \times 7 \times 7 = 343 \). So, \( s=\sqrt[3]{343}=7 \).

Answer:

The length of its side is \( 7 \, \text{cm} \).