Question

A circular disc is divided into 6 equal sectors. If the area of one sector is 66cm², what is the radius of the disc ?

• A. 10 cm
• B. 15.32 cm
• C. 11.22 cm
• D. 13 cm

Answer 1

Answer:

C. 11.22 cm

A circular disc is divided into 6 equal sectors, so the area of one sector is:

$\frac{1}{6}\times \text{Area of circle}=66$

Therefore, the area of the full circle is:

$\text{Area of circle}=66\times6=396\text{ cm}^2$

Using the formula:

$\text{Area of circle}=\pi r^2$
$\pi r^2=396$

Using $(\pi=\frac{22}{7}):$

$\frac{22}{7}r^2=396$

$r^2=\frac{396\times7}{22}$
$r^2=126$
$r=\sqrt{126}=3\sqrt{14}$

$r\approx11.22$