Circles - Using π - Level 6

Practise using pi to calculate various circle measurements.

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This is 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. 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.

 1) What is the area of this composite shape made up of a rectangle and a semicircle? The radius of the semicircle is 9cm and the width of the rectangle is 7cm. Working: cm2 2) Find the area shaded in red which is what is left when four identical quarter circles are taken away from a square. The length of a side of the square is twice the length of the radius of a quarter circle. cm2 3) What is the circumference of this plate divided by its radius? cm 4) A square is inscribed in a circle of radius 7.4cm. Calculate the area shaded red. mm2 5) The area of the circular base of this carton is half the area of the circular top. Find the diameter of the top if the diameter of the bottom is 5.8cm. cm 6) The radius of a bicycle wheel is 35cm. It rotated 17132 times during a particular journey. How long was that journey? Give your answer in kilometres. km 7) A playground is in the shape of a square surrounded by four semi circles. At its widest it is 35 metres wide. What is the length of the perimeter of the playground? m 8) A lawn is in the shape of a rectangle with a semicircle at either end. The width of the rectangle is 8.2m and the distance between the two semi circles (i.e., the length of the rectangle) is 5m. Find the area of the lawn. m2 9) The radius of a sector is 6.5cm and its area is 62cm2. What is the angle between the two straight edges of the sector. degrees 10) Can you calculate the area of this shape? Your clues are: minor radius: 3.5cm, major radius: 7.1cm and angle: 264o. cm2
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This is Circles - Using pi level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 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.

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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.

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]

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.

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