Question

question 11: standard g.c.2 1
geometry
to solve for sector area we need the central angle in degrees and the ______.
a. radius
b. chord
c. diameter
d. tangent line
question 12: standard g.c.2 1
if the radius of a circle is 2 and the central angle is 40 degrees, what is the sector area?
a. 1.4
b. 3.2
c. 0.64
d. 2.8

Explanation:

Question 11

The formula for the area of a sector of a circle is \( A=\frac{\theta}{360}\times\pi r^{2} \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle. A chord is a line segment connecting two points on the circle, a diameter is a special chord passing through the center (equal to \( 2r \)), and a tangent line touches the circle at only one point. None of chord, diameter (other than through radius), or tangent line are directly used in the sector area formula with central angle. So we need the radius.

Step 1: Recall the sector area formula

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

Step 2: Substitute the given values

We are given that \( r = 2 \) and \( \theta=40^{\circ} \). Substituting these values into the formula:
\( A=\frac{40}{360}\times\pi\times(2)^{2} \)
First, calculate \( (2)^{2}=4 \). Then, \( \frac{40}{360}=\frac{1}{9} \). So the formula becomes \( A=\frac{1}{9}\times\pi\times4 \)

Step 3: Calculate the value

\( \frac{4\pi}{9}\approx\frac{4\times3.14}{9}=\frac{12.56}{9}\approx1.4 \)

Answer:

a. Radius

Question 12