Calculate the volume of the cubes given side length or face area.

Question

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Calculate the volume of each

a)

Identify the side length of the cube.
The side length $s = 5 \text{ cm}$ .
Use the formula for the volume of a cube, $V = s^3$ .
$V = (5 \text{ cm})^3$
Calculate the volume.
$V = 5 \times 5 \times 5 \text{ cm}^3$ $V = 125 \text{ cm}^3$
The volume of the cube is $\boxed{\text{125 cm}^3}$ .

Find the volume of the cubes

a)
Find the side length of the cube from the given face area.
The area of one face $A = 49 \text{ m}^2$ .
For a cube, each face is a square, so $A = s^2$ .
$s^2 = 49 \text{ m}^2$ $s = \sqrt{49 \text{ m}^2}$ $s = 7 \text{ m}$
Use the formula for the volume of a cube, $V = s^3$ .
$V = (7 \text{ m})^3$
Calculate the volume.
$V = 7 \times 7 \times 7 \text{ m}^3$ $V = 343 \text{ m}^3$
The volume of the cube is $\boxed{\text{343 m}^3}$ .

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