Question

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.
33.49 cm²
blank 1 33.49
question 4 (1 point)
a circular stage has a radius of 6 m. a spotlight shines on a 75° sector of the stage.
what is the area of the lit region?
m²
blank 1:
question 5 (1 point)
a pie chart has a radius of 5 inches. one category takes up 90° of the chart.
find the area of that category
in²
blank 1

Explanation:

Question 4

Step1: Recall sector area formula

The formula for the area of a sector with radius \( r \) and central angle \( \theta \) (in degrees) is \( A=\frac{\theta}{360}\times\pi r^{2} \). Here, \( r = 6\space m \) and \( \theta=75^{\circ} \).

Step2: Substitute values into formula

First, calculate \( r^{2}=6^{2} = 36 \). Then, \( \frac{\theta}{360}=\frac{75}{360}=\frac{5}{24} \). Now, multiply by \( \pi r^{2} \): \( A=\frac{5}{24}\times\pi\times36 \).

Step3: Simplify the expression

\( \frac{5}{24}\times36\pi=\frac{5\times36}{24}\pi=\frac{180}{24}\pi = 7.5\pi\approx7.5\times3.14 = 23.55 \) (or keep it in terms of \( \pi \) as \( 7.5\pi \) or \( \frac{15}{2}\pi \)).

Step1: Recall sector area formula

The formula for the area of a sector with radius \( r \) and central angle \( \theta \) (in degrees) is \( A = \frac{\theta}{360}\times\pi r^{2} \). Here, \( r=5\space \text{inches} \) and \( \theta = 90^{\circ} \).

Step2: Substitute values into formula

First, \( r^{2}=5^{2}=25 \). Then, \( \frac{\theta}{360}=\frac{90}{360}=\frac{1}{4} \). Now, \( A=\frac{1}{4}\times\pi\times25 \).

Step3: Simplify the expression

\( A=\frac{25}{4}\pi = 6.25\pi\approx6.25\times3.14 = 19.625 \).

Answer:

\( 7.5\pi \) (or approximately \( 23.55 \))

Question 5