Transum Software

Circles - Using π - Level 2

Practise using pi to calculate various circle measurements.

Menu Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Exam Help More

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 8.4cm.

cm Correct Wrong

Calculate the diameter of a circle if the circumference is 5cm.

cm Correct Wrong

Calculate the radius of a circle if the circumference is 7.4cm.

cm Correct Wrong

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

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 4.8cm 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 492cm. What is the radius of the table cloth?

cm Correct Wrong

Jan likes to go jogging around circular park. One complete circuit is 600m. 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

23 coins are laid flat end to end to form a long line of coins. If all of the coins have circumferences of 9.5mm, calculate the total length of the line. Give your answer in centimetres.

cm Correct Wrong

Check

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

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, :

"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Lemon Law

Lemon Law

A fascinating digit changing challenge. Change the numbers on the apples so that the number on the lemon is the given total. Can you figure out, by understanding place value, how this works?

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Fermat's Library, Twitter

Wednesday, January 9, 2019

Transum.org is a proud supporter of the kidSAFE Seal Program

Description of Levels

Close

Close

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.

Log in Sign up

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.

Log in Sign up

Close

Close