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.
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. |
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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. |
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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. |
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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 |