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The radius of a circle is given as 5cm subject to an error of 0.1cm. What is the...


Question

The radius of a circle is given as 5cm subject to an error of 0.1cm. What is the percentage error in the area of the circle?

Options

A) \(\frac{1}{25}\)

B) \(\frac{1}{4}\)

C) 4

D) 25

The correct answer is A.

Explanation:

Area = \(\pi r^2 = \pi \times 5 \times 5 = 25\pi\)
Area error = \(\pi \times 0.1^2 = 0.01\pi\)
\(\therefore\) % error = \(\cfrac{0.01\pi}{25\pi} \times 10\)
\(= \cfrac{0.01}{25} \times 100 = \cfrac{1}{25}\)

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Dicussion (1)

  • Area = \(\pi r^2 = \pi \times 5 \times 5 = 25\pi\)
    Area error = \(\pi \times 0.1^2 = 0.01\pi\)
    \(\therefore\) % error = \(\cfrac{0.01\pi}{25\pi} \times 10\)
    \(= \cfrac{0.01}{25} \times 100 = \cfrac{1}{25}\)

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