Calculating Exactly with Pi

Calculating Exactly with Pi

GCSE(H),

When carrying out calculations with pi (π), the most accurate answer is obtained by evaluating π at the end of the calculation.

The value for π is given as 3.14 in exams. Calculators give a more accurate figure.

Examples

1. Giving the answer in terms of π, what is the surface area of a sphere of diameter 60cm? The formula for the surface area of a sphere is A = 4πr2.

Answer: 240π cm2

The radius of the sphere is half the diameter, or 30cm.

Using the formula, A = 4 x π x 302

A = 4 x π x 900

A = 3600π cm2. The answer is to be left in terms of π.

2. A surface radar is sweeping an arc of 60º; with a range of 12km. What is the surface area being swept by the radar? Give your answer in terms of π.

Answer: 24π

Area of a circle is given by A = πr2.

Area of whole circle = π x 122 = 144π

But the radar is sweeping 60/360º of a whole circle, so area being swept is 144π x `frac(60)(360)`

= 144π ÷ 6 = 24π