Question

If the area of sector is 105cm2 and length of arc is 30cm find the radius

Answer 1

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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