Lesson 9 Exit G2 Area of Sectors

Front

What is the formula for the area of a sector?

Back

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

Front

How do you find the area of a shaded region in a circle?

Back

To find the area of a shaded region, subtract the area of the unshaded part from the total area of the circle.

Front

What is the relationship between the radius and diameter of a circle?

Back

The diameter is twice the radius: \( d = 2r \).

Front

If the diameter of a circle is 38 ft, what is the radius?

Back

The radius is half of the diameter: \( r = \frac{38}{2} = 19 \) ft.

Front

What is the area of a circle with a radius of 19 ft?

Back

The area is given by \( A = \pi r^2 = \pi (19)^2 \approx 1134.11 \) ft².

Front

How do you convert the area of a sector from radians to degrees?

Back

To convert from radians to degrees, use the formula: \( \text{degrees} = \text{radians} \times \frac{180}{\pi} \).

Front

What is the area of a sector with a central angle of 90 degrees and a radius of 10 cm?

Back

The area is \( A = \frac{90}{360} \times \pi (10)^2 = \frac{1}{4} \times 100\pi = 25\pi \approx 78.54 \) cm².

Front

What does it mean to round to the nearest hundredth?

Back

Rounding to the nearest hundredth means to keep two decimal places in the number.

Front

How do you find the exact area of a sector in terms of \( \pi \)?

Back

Use the formula: \( A = \frac{\theta}{360} \times \pi r^2 \) and express the area in terms of \( \pi \) without calculating its numerical value.

Front

What is the area of a sector with a central angle of 180 degrees and a radius of 7 cm?

Back

The area is \( A = \frac{180}{360} \times \pi (7)^2 = \frac{1}{2} \times 49\pi = 24.5\pi \approx 76.96 \) cm².