G.C.5 Arc Length Sector Area Remediation

Front

What is the formula for the area of a sector?

Back

Area = (θ/360) * π * r², where θ is the angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5

Front

How do you find the area of a sector with a 90° angle and a radius of 8 units?

Back

Area = (90/360) * π * 8² = 16π units².

Tags

CCSS.HSG.C.B.5

Front

What is the relationship between arc length and radius in a circle?

Back

Arc Length = (θ/360) * 2πr, where θ is the angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5

Front

If a circle has a radius of 10 cm, what is the arc length of a 60° sector?

Back

Arc Length = (60/360) * 2π * 10 = (1/6) * 20π = (10/3)π cm.

Tags

CCSS.HSG.C.B.5

Front

What is the area of a circle with a radius of 5 inches?

Back

Area = π * r² = π * 5² = 25π square inches.

Tags

CCSS.7.G.B.4

Front

How do you calculate the radius if the area of a sector is 32π and the angle is 90°?

Back

Area = (90/360) * π * r²; 32π = (1/4) * π * r²; r² = 128; r = 8 inches.

Tags

CCSS.HSG.C.B.5

Front

What is the formula for arc length?

Back

Arc Length = (θ/360) * 2πr.

Tags

CCSS.HSG.C.B.5

Front

If the radius of a circle is doubled, how does the area change?

Back

The area increases by a factor of 4, since Area = π * r².

Tags

CCSS.7.G.B.4

Front

What is the area of a sector with a 120° angle and a radius of 12 units?

Back

Area = (120/360) * π * 12² = (1/3) * 144π = 48π units².

Tags

CCSS.HSG.C.B.5

Front

What is the formula for finding the area of a segment in a circle?

Back

Area of Segment = Area of Sector - Area of Triangle.

Tags

CCSS.HSG.C.B.5