| Shape | Formula |
|---|---|
| Rectangle | $P = 2(l + w)$ |
| Square | $P = 4s$ |
| Circle (circumference) | $C = 2\pi r = \pi d$ |
| Triangle | $P = a + b + c$ |
| Shape | Formula |
|---|---|
| Rectangle | $A = lw$ |
| Square | $A = s^2$ |
| Triangle | $A = \tfrac{1}{2}bh$ |
| Parallelogram | $A = bh$ |
| Trapezium | $A = \tfrac{1}{2}(a+b)h$ |
| Circle | $A = \pi r^2$ |
| Sector | $A = \tfrac{\theta}{360}\pi r^2$ |
| Solid | Formula |
|---|---|
| Rectangular prism | $V = lwh$ |
| Cylinder | $V = \pi r^2 h$ |
| Cone | $V = \tfrac{1}{3}\pi r^2 h$ |
| Sphere | $V = \tfrac{4}{3}\pi r^3$ |
| Pyramid | $V = \tfrac{1}{3}Ah$ (where $A$ = base area) |
| Solid | Formula |
|---|---|
| Rectangular prism | $SA = 2(lw + lh + wh)$ |
| Cylinder | $SA = 2\pi r^2 + 2\pi r h$ |
| Sphere | $SA = 4\pi r^2$ |
| Cone | $SA = \pi r^2 + \pi r l$ (where $l$ = slant height) |
A water tank is cylindrical with radius $r = 0.6$ m and height $h = 1.4$ m.
$$V = \pi r^2 h = \pi (0.6)^2 (1.4) = \pi \times 0.36 \times 1.4 = 0.504\pi \approx 1.583 \text{ m}^3$$
Capacity: \$1.583 \times 1000 = 1583 \text{ L}$.
$$SA = 2\pi(0.6)^2 + 2\pi(0.6)(1.4) = 2\pi(0.36 + 0.84) = 2\pi(1.2) \approx 7.54 \text{ m}^2$$
A garden bed consists of a rectangle (5 m × 3 m) with a semicircle of diameter 3 m on one end.
$$A_{\text{rect}} = 5 \times 3 = 15 \text{ m}^2$$
$$A_{\text{semicircle}} = \tfrac{1}{2}\pi\left(\tfrac{3}{2}\right)^2 = \tfrac{1}{2}\pi(1.5)^2 = \tfrac{1}{2}\pi(2.25) \approx 3.53 \text{ m}^2$$
$$A_{\text{total}} \approx 15 + 3.53 = 18.53 \text{ m}^2$$
EXAM TIP: Always include units in every line of working. Examiners award method marks partly based on correct unit handling. State the formula, substitute values, then evaluate.
COMMON MISTAKE: Using the diameter instead of the radius in circle/cylinder/sphere formulas. Double-check: $r = d/2$.
