Surface Area of Solids

A cube has 6 identical square faces, so surface area = $6\times (\text{side length}{)}^2$.

Each face has area $4\times 4=16{\text{ cm}}^2$.

Surface area = $6\times 16=96{\text{ cm}}^2$.

Take care not to give the volume instead: that would be $4^3=64{\text{ cm}}^3$, a different quantity in different units.

The top face is a rectangle. Its two edges are the length, $6\text{m}$, and the depth, $2\text{m}$. The $3\text{m}$ edge is the height of the cuboid and is not part of the top face.

Area = length × width = $6\times 2=12{\text{ m}}^2$.

Area is measured in square metres (m²) because two lengths have been multiplied together.

A cube has 6 identical square faces, so its surface area is $6s^2$, where $s$ is the length of one side.

Set up the equation: $6s^2=150$, so $s^2=150÷6=25$.

Now take the square root: $s=\sqrt{25}=5\text{ cm}$. Check: $6\times 5^2=6\times 25=150{\text{ cm}}^2$.

A cuboid has three pairs of identical rectangular faces, so the total surface area is $2\times (lw+lh+wh)$.

Here: $2\times (12\times 7+12\times 5+7\times 5)=2\times (84+60+35)=2\times 179=358{\text{ cm}}^2$.

Remember to double: the three faces you picture facing you are matched by three identical hidden faces behind them.

A cuboid has three pairs of identical rectangular faces, so the total surface area is $2\times (lw+lh+wh)$.

Here: $2\times (15\times 10+15\times 8+10\times 8)=2\times (150+120+80)=2\times 350=700{\text{ cm}}^2$.

The doubling matters: every face you can see has an identical partner on the opposite side.

First find the total surface area: $2\times (lw+lh+wh)=2\times (12\times 6+12\times 8+6\times 8)=2\times (72+96+48)=432{\text{ m}}^2$.

The top face is a $12\text{ m}$ by $6\text{ m}$ rectangle, so its area is $72{\text{ m}}^2$.

Excluding the top face: $432-72=360{\text{ m}}^2$. Note that the base is still included: only the top is left out.