Question

Write a formula for r in terms of 0 based on the image below.

Answer 1

Given:

The arc length for the given sector is 7π

The central angle for the given sector is θ

The radius of the circle is r.

We need to determine the formula for r in terms of θ

Formula for r:

The formula for r in terms of θ can be determined using the arc length formula,

$S=r \theta$

Substituting the values, we have;

$7 \pi =r \theta$

Dividing both sides by θ, we get;

$\frac{7 \pi}{\theta}=r$

Thus, the formula for r in terms of θ is $\frac{7 \pi}{\theta}$