Questions and Answers
How is the area of a semicircle found?
Take half the area of the whole circle.
Find the length of an arc of 40° in a circle with an 8 inch radius.
16 π/9 inches
What is the radius of a circle in which a 30° arc is 2 π inches long?
12 inches
What is the degree measure of an arc 4 π ft long in a circle of radius 10 ft?
Signup and view all the answers
A bicycle wheel with radius 26" rotates through an arc that measures 80°. What is the length of the arc of the tire that touched the ground?
Signup and view all the answers
If the length of an arc is 12 π inches and the radius of the circle is 10 inches, what is the measure of the arc?
Signup and view all the answers
What part of the circumference is an arc whose measure is 30°?
Signup and view all the answers
What is the area of a sector with radius 10" and measure of arc equal to 45°?
Signup and view all the answers
What is the area of a sector with measure of arc equal to 90° and radius equal to 1 foot?
Signup and view all the answers
What is the area of a sector with radius equal to 8 and measure of arc equal to 300°?
Signup and view all the answers
In a circle of radius 10 cm, a sector has an area of 40 π sq.centimeters. What is the degree measure of the arc of the sector?
Signup and view all the answers
What is the radius of a circle with a sector area of 7 π sq.ft and an arc whose measure is 70°?
Signup and view all the answers
A 10" diameter pumpkin pie is cut into six equal servings. What is the area of the top of each piece of pie?
Signup and view all the answers
An equilateral triangle with a side of 2√3 is inscribed in a circle. What is the area of one of the sectors formed by the radii to the vertices of the triangle?
Signup and view all the answers
A square with sides of 3√2 is inscribed in a circle. What is the area of one of the sectors formed by the radii to the vertices of the square?
Signup and view all the answers
Study Notes
Area of Semicircles and Sectors
- The area of a semicircle is calculated as half the area of a full circle.
Arc Length Calculations
- For a circle with an 8-inch radius, the length of a 40° arc is 16 π/9 inches.
- In a circle where a 30° arc is measured as 2 π inches long, the radius is determined to be 12 inches.
- An arc measuring 4 π ft in a circle with a radius of 10 ft corresponds to a degree measure of 72°.
- A bicycle wheel with a radius of 26 inches rotates through an 80° arc, resulting in an arc length of 11.56 π inches.
Arc Measure Derivations
- Given an arc length of 12 π inches and a circle radius of 10 inches, the degree measure of the arc is found to be 216 degrees.
- An arc measuring 30° accounts for 1/12 of the total circumference of the circle.
Area of Sectors
- The area of a sector with a radius of 10 inches and an arc measure of 45° is 12.5 π square inches.
- For a sector with a 90° arc and a radius of 1 foot, the area is calculated as 0.25 π square inches.
- A sector with a radius of 8 and an arc measure of 300° has an area of 53.3 π square inches.
Sector Area and Arc Measures
- In a circle where the radius is 10 cm, a sector area of 40 π square centimeters corresponds to a degree measure of 144°.
- A sector area of 7 π square feet with an arc measure of 70° indicates a radius of 6 feet.
Practical Applications
- For a 10" diameter pumpkin pie cut into six equal servings, the area of each piece is approximately 4.17 π square inches.
- An equilateral triangle inscribed in a circle with sides of 2√3 yields a sector area of 1.33 π square inches for one of its sectors.
- A square inscribed in a circle with sides of 3√2 results in a sector area of 2.25 π square inches.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the concepts of area calculations for semicircles and sectors, as well as arc length computations. Test your understanding of these geometric principles through a series of problems involving circles' measurements and properties. Challenge your skills with real-world applications related to arcs and sectors.
