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Answers in terms of π

Answers in terms of π

A more accurate answer, when calculating circle-based objects, can be obtained by not using a value of `π`, but to leave it as a constant.

Questions may ask for the answer to be given in terms of `π`. In this instance, do not use a value for `π`, show the answer instead as a multiple of `π`.

Example 1

A circle has a radius of 8 cm. What is the area of the circle?

Give your answer in terms of `π`.

Area of a circle: A ` = pir^2`
Substitute: A ` = pi xx 8^2`
In terms of `pi`: A ` = 64pi`

Answer: 64`π` cm2

Example 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`.

Area of a circle is given by A = `π`r2.

Area of whole circle = `π` x 122 = 144`π`

But the radar is sweeping 60/360º of a whole circle,

Area being swept: A = 144`π` x `frac(60)(360)`
= 144`π` ÷ 6
In terms of `pi`: = 24`pi`

Answer: 24`π` km2