Volume and Surface Area: Practice

Surface area adds up flat face areas, and area is measured in square units, so surface area uses square units like $\text{cm}^2$, never cubic units.

A box has a top and bottom, a front and back, and two ends: $6$ flat faces in all. They come in three pairs of equal opposite faces.

A cube is a box with $l = w = h = s$, so multiply the edge by itself three times.

$V = s \times s \times s = s^3$

This is why $s^3$ is read "$s$ cubed."

Cube the edge length.

$V = s^3 = 2^3 = 8 \text{ cm}^3$

The answer is in cubic centimetres.

Unfolding a solid flat gives its net. The net has all the same faces as the solid, so its total area is the solid's surface area.

A cube has $6$ identical square faces, each of area $s^2$.

$S = 6 \times s^2 = 6s^2$

A cube has $6$ square faces of area $s^2$.

$S = 6s^2 = 6 \times 3^2 = 6 \times 9 = 54 \text{ cm}^2$

The unit is square centimetres because surface area sums flat faces.

Stacking copies of the base up to the top gives volume equal to the base area times the height.

$V = (\text{base area}) \times h$

Multiply length, width, and height.

$V = 4 \times 2 \times 3 = 24 \text{ m}^3$

Volume is in cubic metres.

A cylinder's base is a circle of area $\pi r^2$, and volume is base area times height.

$V = \pi r^2 h$

The expression $2\pi r h$ is part of the surface area, not the volume.

Slitting the curved side straight up and unrolling it flattens it into a rectangle. Its height is the cylinder's height and its width is the circumference of the circular end.

Multiply the three dimensions.

$V = 6 \times 1 \times 1 = 6 \text{ cm}^3$

This box is a single row of $6$ unit cubes.