Geometry, Circles: Area of Sectors

Find the length of an arc of 40° in a circle with an 8 inch radius.

16 π/9 inches

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?

2.25 π

A 10" diameter pumpkin pie is cut into six equal servings. What is the area of the top of each piece of pie?

4.17 π square inches

What part of the circumference is an arc whose measure is 30°?

1/12

How is the area of a semicircle found?

Take half the area of the whole circle.

An equilateral triangle with 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?

1.33 π square inches

What is the radius of a circle in which a 30° arc is 2 π inches long?

12 inches

What is the area of a sector with radius 10" and measure of arc equal to 45°?

12.5 π sq. inches

What is the degree measure of an arc 4 π ft. long in a circle of radius 10 ft.?

72°

What is the radius of a circle with a sector area of 7 π sq. ft. and an arc whose measure is 70°?

6 feet

What is the area of a sector with measure of arc equal to 90° and radius equal to 1 foot?

0.25 π sq. inches

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?

11.56 π inches

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?

144°

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?

216 degrees

What is the area of a sector with radius equal to 8 and measure of arc equal to 300°?

53.3 π