# If the area of a sector of a circle bounded by an arc

Question:

If the area of a sector of a circle bounded by an arc of length 5π  cm is equal to 20π cm2, then the radius of the circle

(a) 12 cm

(b) 16 cm

(c) 8 cm

(d) 10 cm

Solution:

We have given length of the arc and area of the sector bounded by that arc and we are asked to find the radius of the circle.

If l is the length of the arc, A is the area of the arc and r is the radius of the circle, then we know the expression of the area of the sector in terms of the length of the arc and radius of the circle.

Area of the sector $=\frac{1}{2} l r$

Now we will substitute the corresponding values of length of the arc and area of the sector.

$\therefore 20 \pi=\frac{1}{2} \times 5 \pi \times r$

Multiplying both sides of the equation by 2 we get,

$40 \pi=5 \pi \times r$

Dividing both sides of the equation by we get

$r=8$

Therefore, radius of the circle is $8 \mathrm{~cm}$.

Hence, the correct answer is option (c).