Question

4. If the area of a sector of a circle is 8π and with central angle 45 degrees, what is the radius of the circle?
a) 4 b) 8 c) 16 d) 64

Answer 1

Given:

If the area of a sector of a circle is 8π and with central angle 45 degrees

To find:

The radius of the circle

Solution:

The area of the sector of the circle, A = 8π

The central angle, θ = 45°

Let "r" represent the radius of the circle.

Since the value of θ is in terms of degrees so, we know the formula of the sector of a circle will be as follows:

$\bigstar\boxed{\bold{Area\:of\:sector = \frac{\theta}{360\°} \times \pi r^2 }}\bigstar$

Now, substituting the given values in the formula of the sector of a circle above, we get

$A = \frac{\theta}{360\°} \times \pi r^2$

$\implies 8 \pi = \frac{45\°}{360\°} \times \pi \times r^2$

$\implies 8 \pi = \frac{1}{8} \times \pi \times r^2$

cancelling π from both sides

$\implies 8= \frac{1}{8} \times r^2$

$\implies r^2 = 8 \times 8$

takin square root on both sides

$\implies r = \sqrt{8 \times 8}$

$\implies \bold{r = 8}$

Thus, the radius of the circle is → option (b) → 8.

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