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Question

From a circular sheet of radius $$4\ cm$$, a circle of radius $$3\ cm$$ is removed. Find the area of the remaining sheet. (Take $$\pi =3.14$$)
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Solution

Area of the remaining part$$=$$Area of bigger circle$$-$$Area of the smaller circle.

Consider the bigger circle: Radius $$r=4\ cm$$

Area$$=\pi{r}^{2}=3.14\times{4}^{2}=\dfrac{314}{100}\times 16=\dfrac{5024}{100}=50.24\ {cm}^{2}$$

Consider the smaller circle: Radius $$r=3\ cm$$

Area$$=\pi{r}^{2}=3.14\times{3}^{2}=\dfrac{314}{100}\times 9=\dfrac{2826}{100}=28.26\ {cm}^{2}$$

Area of the remaining part$$=$$Area of bigger circle$$-$$Area of the smaller circle.

$$=50.24\ {cm}^{2}-28.26\ {cm}^{2}=21.98\ {cm}^{2}$$

$$\therefore$$ Area of remaining sheet is $$21.98\ {cm}^{2}$$

Mathematics

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