Question

difference between the circumference and radius of a circle is 74 cm. find the area of the circle?

Answer 1

the answer is in the given attachment for any queries use comment box .

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Answer 2

$\mathbf{Circumference \: \: of \: \: circle = 2\pi \: r \: } \: \: \: \: \: \: \: \: \: \: \\ \\ \mathbf{ radius \: of \: circle \: = r}$



Given, Difference between circumference and radius = 74


$2\pi \: r - r = 74 \\ \\ = > r(2\pi \: - 1) = 74 \\ \\ = > r( \frac{44}{7} - 1) = 74 \\ \\ \\ = > r ( \frac{44 - 7}{7} ) = 74 \\ \\ \\ = > r( \frac{37}{7} ) = 74 \\ \\ \\ = > r = \frac{74 \times 7}{37} \\ \\ \\ = > r = 2 \times 7 \\ \\ \\ = > r = 14 \: cm$





Hence,


$Area of circle = \pi {r}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (as \: we \: know \: ) \\ \\ = > Area \: \: of \: \: circle = \frac{22}{7} \times 14 \times 14 \\ \\ \\ = > Area \: \: of \: \: circle = 22 \times 2 \times 14 \\ \\ Area \: \: of \: \: circle = 22 \times 28 \\ \\ Area \: \: of \: \: circle = 616 {cm}^{2}$