Question

use the diagram to answer the questions. what is the area of the circle in terms of pi? □▼π units² what is the measure of the central angle of the shaded sector? □▼° what is the area of the shaded sector rounded to the nearest whole number? □▼ units² (diagram: circle with center a, points c, t on circumference, radius 11, unshaded angle 217°)

Explanation:

First Question: Area of the circle in terms of pi

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Identify the radius

From the diagram, the radius \( r = 11 \) units.

Step3: Substitute the radius into the formula

Substitute \( r = 11 \) into \( A = \pi r^2 \), we get \( A = \pi \times 11^2 \).

Step4: Calculate \( 11^2 \)

\( 11^2 = 121 \), so the area of the circle is \( 121\pi \) square units.

Step1: Recall the total degrees in a circle

A full circle has \( 360^\circ \).

Step2: Find the central angle of the unshaded sector

From the diagram, the unshaded sector has a central angle of \( 217^\circ \).

Step3: Calculate the central angle of the shaded sector

Subtract the unshaded angle from \( 360^\circ \): \( 360 - 217 = 143 \). So the central angle of the shaded sector is \( 143^\circ \).

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \( A_{\text{sector}}=\frac{\theta}{360}\times\pi r^2 \), where \( \theta \) is the central angle of the sector and \( r \) is the radius of the circle.

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

We know \( \theta = 143^\circ \) (from the second question) and \( r = 11 \) (from the first question), and \( \pi r^2 = 121\pi \) (from the first question).

Step3: Substitute the values into the sector area formula

\( A_{\text{sector}}=\frac{143}{360}\times121\pi \).

Step4: Calculate the value

First, calculate \( \frac{143}{360}\times121 \approx \frac{143\times121}{360}=\frac{17303}{360}\approx 48.0639 \). Then multiply by \( \pi \) (using \( \pi\approx3.1416 \)): \( 48.0639\times3.1416\approx 151 \).

Answer:

\( 121 \)

Second Question: Measure of the central angle of the shaded sector