Question

in circle h with m∠ghj = 46° and gh = 11, find the area of sector ghj. round to the nearest hundredth.

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle with radius \( r \) and central angle \( \theta \) (in degrees) is \( A=\frac{\theta}{360}\times\pi r^{2} \).

Step2: Identify the values of \( \theta \) and \( r \)

We are given that the central angle \( m\angle GHJ = 46^{\circ} \), so \( \theta = 46^{\circ} \). The radius \( r \) of the circle is equal to \( GH \), and \( GH = 11 \), so \( r = 11 \).

Step3: Substitute the values into the formula

Substitute \( \theta = 46^{\circ} \) and \( r = 11 \) into the formula \( A=\frac{\theta}{360}\times\pi r^{2} \):

$$ A=\frac{46}{360}\times\pi\times(11)^{2} $$

Step4: Calculate the value

First, calculate \( (11)^{2}=121 \). Then, calculate \( \frac{46}{360}\times\pi\times121 \).

$$ \frac{46}{360}\times121\times\pi=\frac{46\times121}{360}\times\pi=\frac{5566}{360}\times\pi\approx\frac{5566}{360}\times3.14159 $$

Calculate \( \frac{5566}{360}\approx15.4611 \), then \( 15.4611\times3.14159\approx48.57 \) (rounded to the nearest hundredth).

Answer:

\( 48.57 \)