Calculate the area of the shaded region

Reference no: EM132518691

Part -1

Question 1.

The diagram shows a sector of a circle, centre O. The radius of the circle is 13 cm.
The angle of the sector is 150°.
Calculate the area of the sector.
Give your answer correct to 3 significant figures.

.............................................. cm2
Question 2.

The diagram shows a sector of a circle, centre O, radius 10 cm. The arc length of the sector is 15 cm.

Calculate the area of the sector.

.......................... cm2

Question 3.

OAB is a sector of a circle, centre O. Angle AOB = 60º.
OA = OB = 12 cm.
Work out the length of the arc AB.

Question 4.

Diagram NOT accurately drawn
The diagram shows a sector of a circle, centre O.
The radius of the circle is 6 cm. Angle AOB = 120°.
Work out the perimeter of the sector.

Question 5.

Diagram NOT accurately drawn The diagram shows an equilateral triangle ABC with sides of length 6 cm.
P is the midpoint of AB. Q is the midpoint of AC.
APQ is a sector of a circle, centre A.

Calculate the area of the shaded region.
Give your answer correct to 3 significant figures.

Question 6.

The diagram shows a sector OABC of a circle with centre O. OA = OC = 10.4 cm.
Angle AOC = 120°.

(a) Calculate the length of the arc ABC of the sector. Give your answer correct to 3 significant figures.

(b) Calculate the area of the shaded segment ABC.

Give your answer correct to 3 significant figures.

Question 7. The diagram shows a sector of a circle with centre O. The radius of the circle is 8 cm.

PRS is an arc of the circle. PS is a chord of the circle. Angle POS = 40°

Calculate the area of the shaded segment.
Give your answer correct to 3 significant figures.

Question 8.

ABC is an arc of a circle centre O with radius 80 m.
AC is a chord of the circle. Angle AOC = 35°.

Calculate the area of the shaded region.
Give your answer correct to 3 significant figures.

Part -2

Question 1 Express the following angles in radians, leaving your answers in terms of Π where appropriate.
(i) 45° III) 90° vI) 120° (iv) 75°
(v) 300° (vi) 23° vii) 450° (viii) 209°
(ix) 150° ix) 7.2°

Question 2 Express the following angles in degrees, using a suitable approximation where necessary.

i) Π/10 ii) 3Π/5 iii) 2 radians iv) 4Π/9
v) 3Π vi) 5Π/3 vii) 0.4 radians viii) 3Π/4
ix) 7Π/3 x) 3Π/7

Question 3 Write the following as fractions, or using square roots.

You should not need your calculator.
(i) sin Π/4 (ii) tan Π/3 (iii) cos Π/6 (iv) cosΠ
(v) tan 3Π/4 (vi) sin2Π/3 (vii) tan4Π/3 cos 3Π/4
(ix) sin 5Π/6 (x) cos5Π/3

Question 4 Solve the following equation for 0 ≤ θ ≤ 2Π, giving your answers as multiples of Π.

(i) cosθ = √3/2 (ii) tanθ = 1 (iii) sin θ = 1/√2
(iv) sin θ = -1/2 (v) cos θ = -1/√2 (vi) tan θ = √3

Part -3:

Question 1. Find the length of arc AB

Question 2. The diameter is 24 cm. Find the length of arc CD

Question 3. The length of arc EF is 5Π in. Find the length of the radius.

Question 4. Find the length of arc XY

Radius: Arc:

Question 5. Each row of the table gives dimensions of a sector of a circle of radius r cm. The angle subtended at the centre of the circle is 0 radians, the arc length of the sector is s cm and its area is A cm2. Copy and complete the table.

r (cm)	0 (rad)	s (cm)	A (cm²)
5	Π/4
8	1
4		2
	Π/3	Π/3
5			10
	0.8	13
	2Π/3		4Π
			4Π

a. The area of a circle is 225Π square inches. Find the area of the sector whose central angle is 45°.
b. The central angle of a sector is 60° and the area of the circle is 144Π . What is the area of the sector?
c. A circle has a radius of 12. Find the area of the sector whose central angle is 120°
d. Find the radius of a circle which has a sector area of 9Π whose central angle is 90°
e. The central angle of a sector is 72° and the sector has an area of 5Π. Find the radius.
f. Find the measure of the central angle of a sector if its area is 5Π and the radius is 6.

CRITICAL THINKING BONUS QUESTION

The diagram shows the cross-section of three pencils, each of radius 3.5 mm, held together by a stretched elastic band. Find

(i) the shaded area

(ii) the stretched length of the band.

Reference no: EM132518691

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