Circles, Arcs & Sectors Practice Questions

Question 1

4 marks

You may use a calculator for this question.

A circular table top has a radius of 45 cm.

(a)

Work out the circumference of the table top.

Give your answer correct to 1 decimal place.

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(b)

Work out the area of the table top.

Give your answer correct to 1 decimal place.

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Question 2

4 marks

Do not use a calculator for this question.

A sector of a circle has radius 9 cm and angle 40°.

(a)

Work out the length of the arc of the sector.

Give your answer in terms of $\pi$ .

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(b)

Work out the area of the sector.

Give your answer in terms of $\pi$ .

/ 2

Question 0

6 marks

You may use a calculator for this question.

A restaurant makes circular pizza bases.

The area of a regular base is 615 cm².

(a)

Work out the diameter of a regular base.

Give your answer correct to the nearest centimetre.

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(b)

The restaurant also makes a large base with a diameter of 36 cm.

Work out the area of a large base as a percentage of the area of a regular base.

Give your answer correct to the nearest whole number.

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Question 0

6 marks

You may use a calculator for this question.

$OAB$ is a sector of a circle with centre $O$ and radius 8 cm.

The perimeter of the sector is 30 cm.

(a)

Work out the size of angle $AOB$ .

Give your answer correct to 1 decimal place.

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(b)

Work out the area of the sector.

Give your answer correct to 3 significant figures.

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Question 0

6 marks

Do not use a calculator for this question.

The diagram shows a shape made from a rectangle and a semicircle.

The rectangle is 10 cm by 6 cm.
The straight edge of the semicircle is one of the 6 cm sides of the rectangle.

(a)

Work out the perimeter of the shape.

Give your answer in the form $a+b\pi$ , where $a$ and $b$ are integers.

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(b)

Work out the area of the shape.

Give your answer as an exact value in terms of $\pi$ .

/ 3

Question 0

6 marks

You may use a calculator for this question.

A metal disc is a circle of radius 12 cm.

Three identical circular holes, each of radius 3.5 cm, are cut out of the disc.

(a)

Work out the area of metal remaining.

Give your answer correct to 3 significant figures.

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(b)

Work out the percentage of the disc that has been cut away.

Give your answer correct to 1 decimal place.

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Question 0

5 marks

You may use a calculator for this question.

The wheels of a bicycle are circles of diameter 66 cm.

(a)

The bicycle travels 1 km in a straight line.

Work out the number of complete revolutions made by a wheel.

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(b)

On another journey a wheel makes 1500 complete revolutions.

Work out the distance travelled, in metres.

Give your answer correct to 3 significant figures.

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Question 0

7 marks

You may use a calculator for this question.

$A$ and $B$ are points on a circle with centre $O$ and radius 9 cm.

Angle $AOB = 110°$ .

The shaded region is the segment bounded by the chord $AB$ and the arc $AB$ .

(a)

Work out the area of the shaded segment.

Give your answer correct to 3 significant figures.

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(b)

Work out the perimeter of the shaded segment.

Give your answer correct to 3 significant figures.

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Question 0

5 marks

You may use a calculator for this question.

A barn stands in a large field of grass.

The barn is a rectangle measuring 5 m by 4 m.

A goat is tied to the corner $G$ of the barn by a rope of length 7 m. The rope is tied to the goat's collar and can slide around the outside walls of the barn. The goat cannot get inside the barn.

Work out the total area of grass that the goat can reach.

Give your answer correct to 3 significant figures.

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Number

Algebra

Ratio, Proportion & Rates of Change

Geometry & Measures

Probability

Statistics

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