Question

question 1 (1 point)
a pizza has a radius of 14 cm. one slice makes a 45° angle at the center.
what is the area of that slice?
______ cm²
blank 1:

question 2 (1 point)
a circular garden has a radius of 10 m. a sprinkler waters a sector measuring 120°
what is the area of the watered region?
______ m²
blank 1

question 3 (1 point)
a clock has a radius of 8 cm. from 12 oclock to 2 oclock, the minute hand sweeps out a 60° sector.
find the area of that sector

Explanation:

Question 1

Step 1: Recall the formula for the area of a sector

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

Step 2: Identify the values of \( \theta \) and \( r \)

Here, \( \theta = 45^{\circ} \) and \( r = 14 \space \text{cm} \).

Step 3: Substitute the values into the formula

First, calculate \( r^{2} \): \( r^{2}=14^{2} = 196 \).
Then, calculate \( \frac{\theta}{360^{\circ}}\times\pi r^{2} \):
\( A=\frac{45^{\circ}}{360^{\circ}}\times\pi\times196 \)
Simplify \( \frac{45^{\circ}}{360^{\circ}}=\frac{1}{8} \)
So, \( A=\frac{1}{8}\times\pi\times196=\frac{196\pi}{8}=\frac{49\pi}{2}\approx\frac{49\times 3.14}{2}=76.93 \)

Step 1: Recall the sector area formula

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

Step 2: Identify \( \theta \) and \( r \)

Here, \( \theta=120^{\circ} \) and \( r = 10 \space \text{m} \).

Step 3: Substitute the values into the formula

First, calculate \( r^{2}=10^{2} = 100 \).
Then, \( A=\frac{120^{\circ}}{360^{\circ}}\times\pi\times100 \)
Simplify \( \frac{120^{\circ}}{360^{\circ}}=\frac{1}{3} \)
So, \( A=\frac{1}{3}\times\pi\times100=\frac{100\pi}{3}\approx\frac{100\times3.14}{3}\approx 104.67 \)

Step 1: Recall the sector area formula

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

Step 2: Identify \( \theta \) and \( r \)

Here, \( \theta = 60^{\circ} \) and \( r=8 \space \text{cm} \).

Step 3: Substitute into the formula

First, calculate \( r^{2}=8^{2}=64 \).
Then, \( A=\frac{60^{\circ}}{360^{\circ}}\times\pi\times64 \)
Simplify \( \frac{60^{\circ}}{360^{\circ}}=\frac{1}{6} \)
So, \( A=\frac{1}{6}\times\pi\times64=\frac{64\pi}{6}=\frac{32\pi}{3}\approx\frac{32\times3.14}{3}\approx 33.49 \)

Answer:

\( 76.93 \) (or \( \frac{49\pi}{2} \approx 76.93 \))

Question 2