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Circles - Using π - Level 5

Practise using pi to calculate various circle measurements.

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Exam-Style Description Help

This is 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. 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.

This is a semicircle. It is exactly half of a circle and has a diameter of 18.2cm. Find the area of this semicircle.

Working:

cm2 Correct Wrong

This is exactly a quarter of a circle and has a radius of 7.3cm. Find the area of this shape.

cm2 Correct Wrong

Calculate the perimeter of this semicircle which has a radius of 7.1cm.

The perimeter is the distance around the shape. You will need to add the length of the half circumference to the straight side (which is a diameter).

cm Correct Wrong

Calculate the perimeter of this shape which is exactly one third of a circle with a radius of 6.1cm.

cm Correct Wrong

These shapes are called sectors. The curved side, part of the circumference of the whole circle, is called an arc. To calculate the length of the arc you will need to know the angle between the two straight sides of the sector.

Calculate the arc length subtended by an angle of 30o and a radius of 9.3cm.

cm Correct Wrong

Calculate the arc length subtended by an angle of 137o and a radius of 7.5cm.

cm Correct Wrong

Calculate the area of the sector with an angle of 146o and a radius of 6.8cm.

cm2 Correct Wrong

Calculate the area of the sector with an angle of 220o and a radius of 8.5cm.

cm2 Correct Wrong

Calculate the perimeter of the sector subtended by an angle of 106o and a radius of 9.9cm.

cm Correct Wrong

Calculate the perimeter of the sector subtended by an angle of 346o and a radius of 7.5cm.

cm Correct Wrong

Check

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

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Description of Levels

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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

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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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