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MathematicsGCSE & IGCSEArea, Perimeter & Volume

Volume of a sphere formula

The volume of a sphere formula as it is used in GCSE Mathematics, taken from the GCSE Mathematics formula sheet.

The formula

V=43πr3V = \tfrac{4}{3}\pi r^3

How to use it in the exam

  • Write the formula down before substituting — most mark schemes award a method mark for a correct, clearly quoted formula.
  • Check every quantity is in consistent units before you substitute, then substitute in one step so the working stays easy to follow.
  • Show the rearrangement rather than jumping to the answer, and give the final value to the accuracy the question asks for.

Related area, perimeter & volume formulas

Circle
A=πr2,C=2πrA = \pi r^2, \quad C = 2\pi r
Area of a trapezium
A=12(a+b)hA = \tfrac{1}{2}(a + b)h
Area of a parallelogram
A=bhA = b h
Volume of a prism / cylinder
V=Across-section×l,V=πr2hV = A_{\text{cross-section}} \times l, \quad V = \pi r^2 h
Volume of a cone
V=13πr2hV = \tfrac{1}{3}\pi r^2 h
Volume of a pyramid
V=13×base area×hV = \tfrac{1}{3} \times \text{base area} \times h
Surface area of a sphere
A=4πr2A = 4\pi r^2
Curved surface of a cone
A=πrlA = \pi r l

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