Volume and Surface Area: Practice

Multiply the three dimensions.

$V = 7 \times 4 \times 5 = 140 \text{ cm}^3$

Volume is in cubic centimetres.

Cube the edge length.

$V = s^3 = 5^3 = 5 \times 5 \times 5 = 125 \text{ cm}^3$

For any prism, volume is base area times height (here the length).

$V = B \times h = 9 \times 8 = 72 \text{ cm}^3$

Find one face of each kind, then double the total.

$lw = 5 \times 4 = 20, \quad lh = 5 \times 2 = 10, \quad wh = 4 \times 2 = 8$

$S = 2(20 + 10 + 8) = 2 \times 38 = 76 \text{ cm}^2$

First find the edge from the volume.

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

Then the surface area is $6s^2$.

$S = 6 \times 2^2 = 6 \times 4 = 24 \text{ cm}^2$

Read the dimensions $6$ cm, $5$ cm, and $4$ cm from the figure and multiply.

$V = 6 \times 5 \times 4 = 120 \text{ cm}^3$

Use $V = \pi r^2 h$. Square the radius.

$r^2 = 2^2 = 4$

$V = 3.14 \times 4 \times 7 = 87.92 \text{ m}^3$

The base area is $3 \times 3 = 9 \text{ cm}^2$. Multiply by the height.

$V = 9 \times 10 = 90 \text{ cm}^3$

The diameter is given, so halve it to get the radius.

$r = \frac{6}{2} = 3 \text{ cm}$

Then $V = \pi r^2 h$.

$V = 3.14 \times 3^2 \times 5 = 3.14 \times 9 \times 5 = 141.3 \text{ cm}^3$

Find one face of each kind, then double the total.

$lw = 10 \times 2 = 20, \quad lh = 10 \times 2 = 20, \quad wh = 2 \times 2 = 4$

$S = 2(20 + 20 + 4) = 2 \times 44 = 88 \text{ cm}^2$

The width of the unrolled side is the circumference of the circular end, $C = 2\pi r$.

$C = 2 \times 3.14 \times 3 = 18.84 \text{ cm}$

That is how far it is around the rim.

Multiply length, width, and depth.

$V = 25 \times 10 \times 2 = 500 \text{ m}^3$

Volume is in cubic metres.