11-3 Areas of Circles and Sectors

You found the circumference of a circle.

• Find areas of circles.

• Find areas of sectors of circles.

Area of a Circle

The formula for area of a circle is:

A = π·r2

A = area r = radius

p. 798

If the radius of ּסC is 3 cm, what is its area? Answer in exact form.

A = π·r2

A = π·32

A = 9π

MANUFACTURING An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches.

The diameter of the umbrella is 72 inches, and the cover must extend 8 inches in each direction. So, the diameter of the cover is 8 + 72 + 8 or 88 inches. Divide by 2 to find that the radius is 44 inches.

Answer: The area of the cover is about 6082 square inches.

Area of a circle

Substitution

Use a calculator.

A. 62.8 ft2

B. 254.5 ft2

C. 314.2 ft2

D. 1256.6 ft2

A swimming pool company manufactures circular covers for above ground pools. If the cover is 1 foot longer than the pool on each side, find the area of the cover.

If the area of ּסC is 49π, what is its diameter?

A = π·r2

49π = π·r2

π π

49 = r2

r = 7

ALGEBRA Find the radius of a circle with an area of 58 square inches.

Answer: The radius of the circle is about 4.3 in.

Area of a circle

Substitution

Divide each side by .

Simplify.4.3 ≈ r

Take the positive squareroot of each side.= r

A. 3.8 in.

B. 4.5 in.

C. 5.7 in.

D. 7.6 in.

ALGEBRA Find the radius of a circle with an area of 45 square inches.

The South Rose window in Notre Dame has a diameter of 12.9 meters. Find the area and circumference of the window.

A = π·r2

A = π(12.9)2

A = 166.41π

A = 522.79 meters2

C = 2πr

C = 2π(12.9)

C = 25.8π

C = 81.05 meters

If the area of ּסM is 121 m2, find its circumference.

A = π·r2

121 = π·r2

π π

38.5 = r2

r = 6.2 m

C = 2πr

C = 2π(6.2)

C = 38.99 m

Mּס

What letter is common to both the area and circumference formulas?

r (radius)

Sector AreaSector area is the

wedge-shaped interior regions of a circle formed by central angles.

A sector of a circle is a region formed by two radii and an arc of circle. ABC is a sector of ּסB

A

BC

Formula for Sector Length

360

degreesarcA 2 r

p. 799

is a central angle of ּסK

The arc covers 125° out of a total of 360° or

JK

L

125° 12 cm

2A r

360

125

Find the area of sector JKL to the nearest tenth.

JKL

1.157360

12512A 2

PIE A pie has a diameter of 9 inches and is cut into 10 congruent slices. What is the area of one slice to the nearest hundredth?

Step 1 Find the arc measure of a pie slice.

Since the pie is equally divided into 10 slices, each slice will have an arc measure of

360 ÷ 10 or 36.

Step 2 Find the radius of the pie. Use this measureto find the area of the sector, or slice.

The diameter is 9 inches, so the radius is 4.5 inches.Area of a sector

x = 36 and r = 4.5

Use a calculator.

Answer: The area of one slice of pie is about 6.36 square in.

A. 16.21 in2

B. 19.24 in2

C. 26.43 in2

D. 38.48 in2

PIZZA A pizza has a diameter of 14 inches and is cut into 8 congruent slices. What is the area of one slice to the nearest hundredth?

11-3 Assignment

Page 801, 8-22 even