If area of sector of a circle is 105 CM square and length of its arc is 30 cm, calculate the radius of the circle.
Answers
Answer:
Step-by-step explanation:
If area of sector of a circle is 105 CM square and the length of its arc is 30 cm, then the radius of the circle is 7 cm.
Step-by-step explanation:
Required formula:
(1) Area of the sector of a circle = [θ/360°]* πr²
(2) Arc length of a circle = [θ/360°]* 2πr
Area of the sector of the circle is given = 105 cm
So, from formula (1) mentioned above, we get
105 = [θ/360°]* πr²….. (i)
Arc length of the circle is given = 30 cm
So, from formula (2) mentioned above, we get
30 = [θ/360°]* 2πr ….. (ii)
On dividing eq. (i) by (ii), we get
[105/30] = [{θ/360°} πr²] / [{θ/360°}2πr]
⇒ [105/30] = [r/2]
⇒ r = [105*2] / [30]
⇒ r = 7 cm
Thus, the radius of the circle is 7 cm.
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