Areas Related to Circles quiz

The area of a sector of angle theta (in degrees) of a circle of radius r is:

The length of an arc of a circle of radius 21 cm subtending an angle of 60 degrees at the centre is:

The angle described by the minute hand of a clock in 15 minutes is:

The area of a quadrant of a circle of radius 14 cm is:

If the area of a sector of a circle is 1/6 of the area of the circle, the central angle of the sector is:

The region between a chord and its corresponding arc is called a:

If the central angle of a minor sector is 80 degrees, the central angle of the corresponding major sector is:

The perimeter of a sector of radius 7 cm and central angle 90 degrees is:

A chord of a circle of radius r subtends an angle of 60 degrees at the centre. The triangle formed by the chord and the two radii is:

If the radius of a circle is doubled and the central angle of a sector is kept the same, the area of the sector becomes:

Find the area of a sector of a circle with radius 6 cm if the angle of the sector is 60 degrees. (Use pi = 22/7) (2 marks)

Find the area of a quadrant of a circle whose circumference is 22 cm. (Use pi = 22/7) (2 marks)

The length of an arc of a circle of radius 21 cm is 22 cm. Find the angle subtended by the arc at the centre. (2 marks)

Show that the area of a sector of radius r with arc length l is (1/2) x l x r. (2 marks)

The hour hand of a clock is 6 cm long. Find the area swept by it between 2 p.m. and 4 p.m. (Use pi = 22/7) (2 marks)

Find the area of the minor segment of a circle of radius 14 cm when the angle of the corresponding sector is 90 degrees. (Use pi = 22/7) (2 marks)

A pendulum 42 cm long swings through an angle of 30 degrees. Find the length of the arc described by its bob. (Use pi = 22/7) (2 marks)

The area of a sector of a circle of radius 10 cm is 78.5 cm^2. Find the central angle of the sector. (Use pi = 3.14) (2 marks)

Find the area of a major sector of a circle of radius 7 cm if the minor sector has central angle 90 degrees. (Use pi = 22/7) (2 marks)

Two circles have radii in the ratio 2:3. Sectors of equal central angle are cut from them. Find the ratio of the areas of the two sectors. (2 marks)

A chord of a circle of radius 21 cm subtends an angle of 120 degrees at the centre. Find the area of the corresponding segment of the circle. (Use pi = 22/7 and sqrt(3) = 1.73) (3 marks)

A lighthouse spreads a red-coloured light over a sector of angle 80 degrees to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use pi = 3.14) (3 marks)

The minute hand of a clock is 21 cm long. Find (i) the angle it turns through in 20 minutes (ii) the area it sweeps in that time (iii) the distance travelled by its tip. (Use pi = 22/7) (3 marks)

A circular pizza of diameter 28 cm is cut into 8 equal slices. Find (i) the area of each slice (ii) the length of crust on each slice (iii) the perimeter of each slice. (Use pi = 22/7) (3 marks)

A garden sprinkler waters a region in the shape of a sector of radius 14 m by rotating through 120 degrees. Find the area watered. If the sprinkler is set to rotate through 270 degrees, find the additional area watered. (Use pi = 22/7) (3 marks)

Read the passage and answer the questions. A school is designing a circular flower bed of radius 21 m in the middle of its lawn. The bed is divided into 6 equal sectors by radial paths, and each sector is planted with flowers of a different colour. A decorative fence is to be put along the arc of one sector only. (i) Find the central angle of each sector. (ii) Find the area of each sector. (Use pi = 22/7) (iii) Find the length of fencing needed for the arc of one sector and the total cost at Rs 50 per metre. (5 marks)

Read the passage and answer the questions. Two wipers are fitted on the front windscreen of a bus. The wipers do not overlap. Each blade is 21 cm long and sweeps through an angle of 120 degrees. The driver notices that a narrow strip at the bottom of the windscreen is never cleaned. (i) Find the area cleaned by one wiper in one sweep. (Use pi = 22/7) (ii) Find the total area cleaned by both wipers in one sweep. (iii) If the angle swept were reduced to 90 degrees, by how much would the area cleaned by both wipers decrease? (5 marks)

Read the passage and answer the questions. A cow is tied with a rope of length 14 m at one corner of a rectangular field measuring 20 m by 16 m. The farmer wants to know how much grass is available to the cow and how much of the field remains ungrazed. (i) What is the shape of the region the cow can graze, and what is its central angle? (ii) Find the area of the region the cow can graze. (Use pi = 22/7) (iii) Find the area of the field that the cow cannot graze. (5 marks)

Read the passage and answer the questions. An engineer is designing a circular window of radius 28 cm. A horizontal glass bar is fixed as a chord that subtends a right angle at the centre, and the smaller part above the bar is filled with coloured glass. (i) Name the region filled with coloured glass. (ii) Find the area of the sector formed by the chord and the radii. (Use pi = 22/7) (iii) Find the area of the coloured glass. (5 marks)

Read the passage and answer the questions. At a fair, a circular game board of radius 35 cm is painted in 5 equal sectors numbered 1 to 5. A player spins an arrow and wins the prize shown in the sector where it stops. The organiser wants to paint a golden border along the arc of each sector. (i) Find the angle of each sector. (ii) Find the area of each sector. (Use pi = 22/7) (iii) Find the total length of the golden border along all the arcs, and the length of border along one arc. (5 marks)

Draw a circle with centre O and a chord AB subtending an angle theta at O. Label and shade the minor sector, the minor segment and the major segment. Derive the formula for the area of a sector and the length of an arc by using unitary method from the area and circumference of the full circle. Hence find the area of the sector and the arc length when r = 14 cm and theta = 45 degrees. (Use pi = 22/7) (6 marks)

In a circle of radius 21 cm, an arc subtends an angle of 60 degrees at the centre. Draw a labelled figure and find (i) the length of the arc (ii) the area of the sector formed by the arc (iii) the area of the segment formed by the corresponding chord. (Use pi = 22/7 and sqrt(3) = 1.73) (6 marks)

A round table cover has six equal designs on it, each formed by a chord of the circle that subtends an angle of 60 degrees at the centre (the designs are the minor segments between the chord and the arc). The radius of the cover is 28 cm. Draw a rough figure of the cover and find the cost of making the designs at the rate of Rs 0.35 per cm^2. (Use pi = 22/7 and sqrt(3) = 1.7) (6 marks)

Draw a figure of a square ABCD of side 14 cm with four quadrants of radius 7 cm drawn with centres at A, B, C and D. Find the area of the region of the square not covered by the quadrants. Explain why the four quadrants together have the area of one full circle. (Use pi = 22/7) (6 marks)

A chord of a circle of radius 12 cm subtends an angle of 120 degrees at the centre. Draw a labelled figure and find the area of the corresponding minor segment. Then find the area of the major segment, and explain the steps you followed to find the area of triangle OAB using the perpendicular from O to the chord. (Use pi = 3.14 and sqrt(3) = 1.73) (6 marks)