Rukasha Maths

GCSE maths Beta

Area, circles and volume · Revision guide

Foundation · Geometry · 3 pages in the PDF

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Learning objectives

  • Choose area and circumference formulas.
  • Calculate prism volume and give the correct units.

Key ideas

Use a perpendicular height for triangles and parallelograms.

Atriangle=12bh,Aparallelogram=bhA_{\text{triangle}}=\frac12bh,\qquad A_{\text{parallelogram}}=bh

For a trapezium, use the two parallel sides and perpendicular height.

A=12(a+b)hA=\frac12(a+b)h

Distinguish circle area from circumference; radius is half the diameter.

A=πr2,C=2πr=πdA=\pi r^2,\qquad C=2\pi r=\pi d

A prism has a constant cross-section.

V=cross-sectional area×length;Vcylinder=πr2hV=\text{cross-sectional area}\times\text{length};\quad V_{\text{cylinder}}=\pi r^2h

A sector is a fraction of a complete circle.

sector fraction=θ360∘\text{sector fraction}=\frac{\theta}{360^\circ}

Worked examples

Example 1

Find the exact volume of a cylinder with the given radius and height.

r=3 cm,h=8 cm:A=π(3)2=9π cm2r=3\text{ cm},\quad h=8\text{ cm}:\qquad A=\pi(3)^2=9\pi\text{ cm}^2
V=9π×8=72π cm3V=9\pi\times8=72\pi\text{ cm}^3
72π cm372\pi\text{ cm}^3

Example 2

Find the trapezium area from its parallel sides and perpendicular height.

a=5, b=9, h=4 (cm):A=12(5+9)4=28 cm2a=5,\ b=9,\ h=4\text{ (cm)}:\quad A=\frac12(5+9)4=28\text{ cm}^2
28 cm228\text{ cm}^2

Watch out

Use the radius in the circle area formula. Area uses square units; volume uses cubic units.