Ac and BD are two perpendicular diameter of a circle ABCD. Given that the area of the shaded portion is 308 cm^2.calculate : I) the length of AC and the circumference of the circle
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Answer:
AC = 28 cm & Circumference = 88 cm²
Step-by-step explanation:
Given data:
AC & BD are two perpendicular diameters of circle ABCD
Area of the shaded portion = 308 cm²
To find: (i) the length of AC and (ii)the circumference of the circle
Solution:
Let the radius of the circle be “r” cm.
Case (i): Finding the length of AC
Referring to the figure attached below, we have
The area of the shaded region of the circle = ½ * [Area of the circle]
⇒ 308 = ½ * πr² …. [substituting the given value of area]
⇒ r² = [308*2*7]/22
⇒ r = √[196]
⇒ r = 14 cm
Thus,
The length of AC = 2 * r = 2 * 14 = 28 cm
Case (ii): Finding the circumference of the circle
Thus,
The circumference of the circle is given as,
= 2πr
= 2 * 22/7 * 14
= 2* 22 * 2
= 88 cm²
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