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 $sqrt3{343}=$

Explanation:

Step1: Recall volume formula

The volume $V$ of a cube with edge - length $a$ is given by $V=a\times a\times a=a^{3}$. So the volume of a cube is the product of the length of its edge three times.

Step2: Calculate cube - root

We know that if $V = 343$, and $V=a^{3}$, then $a=\sqrt[3]{V}$. Given $V = 343$, we calculate $\sqrt[3]{343}$. Since $7\times7\times7=343$, $\sqrt[3]{343}=7$.

Answer:

In the first three boxes, we put the variable representing the edge - length (let's say $a$), so it's $a$ cm, $a$ cm, $a$ cm. In the last box, the value of $\sqrt[3]{343}$ is $7$.