Volume and surface area
Prisms (lh), cylinders (πr²h), pyramids (⅓Abaseh), spheres (&frac43;πr³), cones (⅓πr²h).
GCSE formula sheets vary by board. Key: prism volume = cross-sectional area × length. Cylinder, cone, pyramid follow with their respective bases.
Worked examples
Cylinder r=3, h=10: V = 9π × 10 = 90π ≈ 282.7 cm³.
Cone r=3, h=4: V = ⅓π×9×4 = 12π ≈ 37.7 cm³.
Sphere r=5: V = &frac43;π×125 ≈ 523.6 cm³.
Frequently asked questions
Surface area of cone?
Curved: πrl (l = slant height); base: πr². Sum for total.
Hemisphere?
Half a sphere: V = ⅔πr³; SA = 2πr² (curved) + πr² (flat) = 3πr² total.