Question

The ratio of the area and circumference of a circle of diameter d is

(a) d (b) $\frac{d}{2}$ (c) $\frac{d}{4}$ (d) 2d

Answer 1

Let r and d be respectively the radius and diameter of the circle. Then
d = 2r
Circumference of circle = 2$\pi$r = $2\pi \times \frac{d}{2}=\pi d$
Area of circle = $\pi$r² = $\pi {\left(\frac{\mathit{d}}{\mathit{2}}\right)}^{\mathit{2}}=\frac{\pi d^2}{4}$
Now
$\frac{\mathrm{Area}\mathrm{of}\mathrm{circle}}{\mathrm{Circumference}\mathrm{of}\mathrm{circle}}=\frac{{\displaystyle \frac{\pi d^2}{4}}}{\pi d}=\frac{d}{4}$
Hence, the correct option is (c)