GCSE Maths, Unit 23, Lesson 5 of 6
Brainlag Plus

Cones, pyramids and spheres

GCSE Maths, Area, perimeter and volume, 25 minutes

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Volume of pyramids, cones, spheres and hemispheres, curved surface areas, slant height by Pythagoras, and frustums and composite solids.

The formulas you are given, and how to use them

Exam papers give these formulas, but you must know which length goes where.

pyramid: V = ⅓ × base area × height
cone: V = ⅓πr²h, curved surface = πrl
sphere: V = 4/3 πr³, surface area = 4πr²

h is the perpendicular height. l is the slant height, along the sloping side. A hemisphere is half a sphere: V = ⅔πr³.

The rest of this lesson and its 8 practice questions are in Plus.

Screen 1 of 4, free to read.

  • 8 exam-style questions, marked as you go, each with a worked solution
  • Anything you get wrong is saved to your flashcards