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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

### Explanation:

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

## 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 = $$\cfrac{0.01\pi}{25\pi} \times 10$$
$$= \cfrac{0.01}{25} \times 100 = \cfrac{1}{25}$$