Question

relate the volume of the cube to the length of each edge. click the icon to view the cube. edge length □ cm × edge length □ cm × edge length □ cm. (sqrt3{343} = square)

Explanation:

Step1: Recall the volume formula of a cube

The volume \( V \) of a cube with edge length \( s \) is given by \( V = s\times s\times s=s^{3} \). So, to find the edge length from the volume, we take the cube root of the volume, i.e., \( s=\sqrt[3]{V} \).

Step2: Calculate the cube root of 343

We know that \( 7\times7\times7 = 343 \), because \( 7\times7 = 49 \) and \( 49\times7=343 \). So, \( \sqrt[3]{343}=7 \).

Step3: Fill in the edge length boxes

Since the edge length of the cube is 7 cm (because \( \sqrt[3]{343} = 7 \)), each of the edge length boxes should be filled with 7.

Answer:

The edge length of the cube is 7 cm, so the three edge length boxes are all 7, and \( \sqrt[3]{343}=\boldsymbol{7} \). So the filled values are: 7 cm \( \times \) 7 cm \( \times \) 7 cm, and \( \sqrt[3]{343} = 7 \).