Question

What is the radius of a sectorwhen 0== 3/8 radians and thearea is 75/16 sq units?

Answer 1

The area of a sector of the circle is given by:

`A=(r^2\cdot\theta)/(2)`

Where:

A = area

r = radius

θ = angle of radians

Substitute the values:

`(75\pi)/(16)=(r^2\cdot(3\pi)/(8))/(2)`

Simplify:

`(75\pi)/(16)=(r^2\cdot3\pi)/(16)`

Solve for r:

`\begin{gathered} (75\pi)/(16)\cdot(16)/(3\pi)=(r^2\cdot3\pi)/(16)\cdot(16)/(3\pi) \\ 25=r^2 \\ r=√(25) \\ r=5 \end{gathered}`

Answer: r = 5 units