Question

1 the volume of a cube is 729 in³. a. what is the length of the edge of the cube? b. what is the area of one of the faces of the cube?

Explanation:

Step1: Recall volume formula for cube

The volume formula of a cube is $V = s^{3}$, where $s$ is the edge - length. Given $V = 729$ in³, we solve for $s$.
$$s^{3}=729$$

Step2: Find the edge - length

Take the cube - root of both sides: $s=\sqrt[3]{729}=9$ in.

Step3: Recall area formula for a square face of cube

The area of one face of a cube (which is a square) is $A=s^{2}$. Since $s = 9$ in, we substitute $s$ into the formula.
$$A = 9^{2}$$

Step4: Calculate the area of the face

$A=81$ in².

Answer:

a. 9 in
b. 81 in²