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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Cumulative Standards Review

Exercise 8 Page 683

A sector of a circle is the region bounded by an arc of the circle and the two radii to the arc's endpoints. The area of a sector of a circle is the product of the area of the circle and the measure of the arc divided by 360.

G

Practice makes perfect

A sector of a circle is the region bounded by an arc of the circle and the two radii to the arc's endpoints.

The area of a sector of a circle is the product of the area of the circle and the measure of the arc divided by 360.

Area of sectorAOB: m AB/360* π r^2 We want to find the area of the sector formed by the arc AB in ⊙ O. We know that the radius of the circle is 30ft and that the measure of the arc AB is 120^(∘).

We have all the information we need to use the formula to find the area of the sector.

A=120/360* π ( 30^2)

▼

Evaluate right-hand side

Calculate power

A=120/360* π (900)

CommutativePropMult

Commutative Property of Multiplication

A=120/360* 900π

MoveRightFacToNum

a/c* b = a* b/c

A = 108 000/360 * π

Calculate quotient

A = 300 π

Use a calculator

A=942.477796...

The area of the sector is approximately 942 ft^2. Therefore, the answer is G.