# A circle contains a sector with an area of 75cm^2 and a central angle of 270°. What is the radius of the circle to two decimal places?

Jul 31, 2018

$5.64 \text{ cm(2dp)}$.

#### Explanation:

Let $r$ be the radius of the circle.

The Area of a sector having central angle $\theta \text{ radian}$ is $\frac{1}{2} {r}^{2} \theta$.

WE have, ${270}^{\circ} = 3 \frac{\pi}{2} \text{ radian}$.

Hence, by what is given, $\frac{1}{2} {r}^{2} \left(3 \frac{\pi}{2}\right) = 75$.

$\therefore {r}^{2} = \frac{75 \times 4}{3 \pi} = \frac{100}{\pi}$.

;. r=10/sqrtpi~~5.64" cm(2dp)".

Jul 31, 2018

$r = 5.64$cm

#### Explanation:

A sector is a fraction of a circle.
The fraction can be determined in three ways:

$\frac{\text{sector angle")/360" "or" "("arc length")/(2pi r)" "or" "("sector area}}{\pi {r}^{2}}$

In this case we are told that $\frac{3}{4}$ of the area of the whole circle is $75 c {m}^{2}$

$\frac{270}{360} \times \pi {r}^{2} = 75$

${r}^{2} = \frac{75 \times 360}{270 \pi}$

${r}^{2} = 31.83$

$r = 5.64$cm