The ratio of the diameter of a circle to the breadth of a rectangle is $7:4$. The area of the circle is $616\text{ cm}^2$. If the length of the rectangle is 6 cm more than its breadth, what is the area of the rectangle?

268 cm²
286 cm²
305 cm²
352 cm²

Correct answer: 352 cm²

Solution

From area of circle, $\pi r^2=616$, so using $\pi=\frac{22}{7}$ gives $r=14$ cm and diameter $=28$ cm. Since diameter : breadth = 7 : 4, breadth of rectangle = $28\times\frac{4}{7}=16$ cm, so length = 22 cm. Therefore, area = $16\times 22=352\text{ cm}^2$.

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