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Volume and surface area
Volume measures the space inside a 3D shape; surface area is the total area of its faces.
Prisms
A prism has the same cross-section all the way through.
Volume = area of cross-section × length
Cuboid: l × w × h. Cylinder: πr2h.
Volume = area of cross-section × length
Cuboid: l × w × h. Cylinder: πr2h.
Surface area
Add the areas of every face. A cuboid has three pairs of identical rectangles.
Cylinder: two circles plus the curved surface: 2πr2 + 2πrh.
Cylinder: two circles plus the curved surface: 2πr2 + 2πrh.
Cones, pyramids and spheres (Higher)
Pyramid or cone: 13 × base area × height.
Sphere: volume 43πr3, surface area 4πr2.
These formulae are usually given in the exam.
Sphere: volume 43πr3, surface area 4πr2.
These formulae are usually given in the exam.
A cylinder has radius 3 cm and height 10 cm. Find its volume to 1 d.p.
- π × 32 × 10
- = 90π
- = 282.7 cm3
Answer: 282.7 cm3
Prism volume = cross-section area × length. Surface area = total of all faces. Cones and pyramids are a third of a prism; sphere V = (4/3)πr3.
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