Surface Area of 3D Objects

≈ 25 min

The surface area of a solid is the total area of all its faces added together — the amount of material you'd need to cover it completely.

Cube (side $s$ ): six equal square faces, so $SA = 6s^2$ .
Rectangular prism ( $l \times w \times h$ ): three pairs of matching faces, so $SA = 2(lw + lh + wh)$ .
Closed cylinder (radius $r$ , height $h$ ): two circular ends plus the curved side that unrolls into a rectangle, so $SA = 2\pi r^2 + 2\pi r h$ .

Worked example. A box $4 \times 3 \times 2$ cm has $SA = 2(4\!\cdot\!3 + 4\!\cdot\!2 + 3\!\cdot\!2) = 2(12 + 8 + 6) = 52$ cm $^2$ .

Find the surface area of a cube with side 4 cm, in cm $^2$ .

What is the formula for the surface area of a closed cylinder (radius $r$ , height $h$ )?

$2\pi r^2 + 2\pi r h$

$\pi r^2 h$

$2\pi r h$

$\pi r^2 + 2\pi r h$

Find the surface area of a rectangular prism measuring $5 \times 3 \times 2$ cm, in cm $^2$ .

A closed cylindrical tank has radius 7 cm and height 10 cm. Using $\pi = \frac{22}{7}$ , find its surface area in cm $^2$ .