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Circles - Using π - Level 2

Practise using pi to calculate various circle measurements.

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This is level 2; find the radius or diameter given the circumference. Give your answers correct to three significant figures. You can earn a trophy if you get at least 7 correct. The diagrams are not drawn to scale.

Calculate the diameter of a circle if the circumference is 7.5cm.

cm Correct Wrong

Calculate the diameter of a circle if the circumference is 3.2cm.

cm Correct Wrong

Calculate the radius of a circle if the circumference is 2.9cm.

cm Correct Wrong

Calculate the radius of a circle if the circumference is 7.1cm.

cm Correct Wrong

A circle is drawn inside a square so its circumference touches each of the four sides of the square. If the circumference of the circle is 5.9cm calculate the length of the sides of the square.

cm Correct Wrong

Two circles are drawn inside a rectangle so their circumferences touch each other and three sides of the rectangle. If the circumferences of the circles are 6.2cm each, calculate the length of the longest sides of the rectangle.

cm Correct Wrong

A circular table cloth has a hem all the way around its perimiter. The length of this hem is 489cm. What is the radius of the table cloth?

cm Correct Wrong

Jan likes to go jogging around circular park. One complete circuit is 900m. Assuming the park is a circle, what is the distance across the circle from the eastern-most point to the western-most point?

m Correct Wrong

The circumference of the Earth is roughly forty thousand kilometres. Use this value to calculate the distance from the surface to the centre of the Earth.

km Correct Wrong

33 coins are laid flat end to end to form a long line of coins. If all of the coins have circumferences of 9.4mm, calculate the total length of the line. Give your answer in centimetres.

cm Correct Wrong


This is Circles - Using pi level 2. You can also try:
Level 1 Level 3 Level 4 Level 5 Level 6 Composites


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Wednesday, January 9, 2019

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Description of Levels



Level 1 - find the circumference given the radius or diameter.

Level 2 - find the radius or diameter given the circumference.

Level 3 - find the area of a circle given either the radius or diameter.

Level 4 - the areas of circles are given, find either the radius, diameter or circumference.

Level 5 - the radius and angle subtended at the centre of the circle are given, find the length of the arc or area of the sector of the circle.

Level 6 - this level has mixed questions about the circle. Most of these questions will require a multi-part calculation once the situation described in the question has been understood.

Areas of composite shapes requires an ability to calculate the areas of other shapes such as rectangles, triangles and trapezia.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Help with circle calculations

Use a calculator for this exercise. All of the calculations you will do involve the number π (pronounced pi) which is roughly equal to 3.141592. You should use the π button on your calculator to get this number into your calculation.

Let r be the radius, d the diameter, C the circumference and A the area of a circle.

C = πd    [i.e., to find the circumference multiply the length of the diameter by pi]

A = πr2    [i.e., to find the area multiply the square of the radius by pi]

Circle attributes

For arcs multiply the circumference by the angle subtended at the centre and divide by 360.

For sector area multiply the circle area by the angle subtended at the centre and divide by 360.

For help using a calculator with circle calculations see Calculator Workout.

For more on this topic see our Circles page.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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