A chord of length 16 cm is at a distance of 6 cm from the centre of a circle. What is the area of the circle, approximately? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 314.29 cm2
The perpendicular from the centre to a chord bisects the chord, so the radius, half the chord and the distance from the centre form a right triangle. The area of a circle is \(\pi r^2\).
Half of the chord \(=16\div2=8\) cm
Radius \(r=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10\) cm
Area \(\displaystyle=\frac{22}{7}\times10^2=\frac{2200}{7}\approx314.29\) cm2
