Area of a Circle and a Sector Flashcards

Questions and Answers

Which statements are true regarding the area of circles and sectors? Check all that apply.

The area of a sector can be used to find the area of a circle.

The area of a sector depends on the ratio of the central angle to the entire circle. (correct)

The area of the entire circle can be used to find the area of a sector. (correct)

The area of a circle depends on the length of the radius. (correct)

Which statement is true regarding the two shaded sectors of circle O?

The area of sector AOB is equal to the area of sector DOC because the central angle measures are equal.

Approximately how much fabric of each color will be needed to make a single parachute canopy?

88.5 ft²

What is the smallest possible area of the tabletop that will fit on Timothy's table base?

113 square inches Signup and view all the answers

What is the largest possible area of the tabletop that will fit on Timothy's table base?

1,662 square inches Signup and view all the answers

What is the ratio of the sector area to the area of the entire circle?

1/5 Signup and view all the answers

If the radius is doubled, what is the effect on the area of sector XYZ?

The sector area will be 4 times greater. Signup and view all the answers

What is the approximate circumference of the circle?

18.8 units Signup and view all the answers

What is the height of the parallelogram?

3 units Signup and view all the answers

What would be the approximate length of the parallelogram if the base were completely straight?

9.4 units Signup and view all the answers

What would make the estimation of the circle's area more precise?

Breaking the circle into more sectors. Signup and view all the answers

What is the area of the circle used to create the parallelogram-like shape to the nearest tenth of a square unit?

28.3 square units Signup and view all the answers

What is the area of the circle in terms of pi?

π units² Signup and view all the answers

What is the measure of the central angle of the shaded sector?

121° Signup and view all the answers

What is the area of the shaded sector rounded to the nearest whole number?

151 units² Signup and view all the answers

What is the sector area created by the hands of a clock with a radius of 9 inches when the time is 4:00?

27π in.^2 Signup and view all the answers

Arc LM on circle O has a measure of 40°. Which statements are true? Check all that apply.

The ratio of the measure of ∠LOM to the measure of the whole circle is 1/9. Signup and view all the answers

What is the approximate area of the entire circle?

113 square units Signup and view all the answers

What is the approximate area of the entire sector created by the central angle ACB?

28 square units Signup and view all the answers

What is the approximate area of the shaded region only?

22 square units Signup and view all the answers

Study Notes

Area of Circles and Sectors

The area of a circle is determined by its radius.
The area of a sector is influenced by the ratio of the central angle to the full circle.
The area of a circle can help calculate the area of a sector, but not the reverse.

Equal Areas of Sectors

Equal central angle measures ensure equal area for sectors within a circle.

Parachute Canopy Fabric Requirements

A semicircular parachute canopy with a radius of 13 feet requires an approximate area of 88.5 ft² for fabric.

Tabletop Area Constraints

The smallest area for a circular tabletop supported by a base with a radius of at least 6 inches is 113 square inches.
The maximum area for a tabletop fitting within a base of a radius of 23 inches is 1,662 square inches.

Sector to Circle Area Ratio

A sector's area can be expressed as a ratio to the full circle's area, exemplified by a ratio of 1/5.

Effect of Doubling the Radius

When the radius of a sector is doubled, its area increases by a factor of four.

Circle Measurements

The approximate circumference of the circle is 18.8 units.
The height of a related parallelogram can be approximated at 3 units.
A straight base of the parallelogram would measure approximately 9.4 units.
Increased precision of the circle's area can be achieved by dividing it into more sectors.
The area of the circle approximates to 28.3 square units.

Circle Area and Sector Calculations

The area of a certain circle can be expressed as π units².
A shaded sector's central angle can either be a specified measurement or in degrees.
The rounded area of the shaded sector can also be determined.

Clock Sector Area

The sector area formed by clock hands at 4:00, with a radius of 9 inches, is calculated as 27π in².

Arc Measurements and Ratios

An arc measuring 40° indicates that the central angle corresponding to that arc is also 40°.
The ratio of the angle formed at the center to the total circle's measurement can be represented as 1/9.
The full circle could be divided into nine equal-area sectors, equivalent to the area of sector LOM.

Circle and Sector Area Calculations

For a circle with a radius of 6 units, the approximate total area is 113 square units.
The approximate area of a sector defined by the central angle ACB is roughly 28 square units, while the shaded area within that sector is about 22 square units.

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Description

Test your understanding of the area of circles and sectors with this flashcard assignment. Evaluate which statements regarding their areas are true, focusing on aspects like radius, central angles, and ratios. Perfect for mastering the concepts before an exam.