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Leave Answers in Terms of Pi

In this worksheet, students will learn how to leave answers in terms of pi.

'Leave Answers in Terms of Pi' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation, Volume and Surface Area Calculations

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Pi time..yey.  Unfortunately not this pie..

This one. Pi, good old pi, or 3.142 as we often use.

In circle work particularly we use  to help with our calculations.  

You may use the  symbol on your calculator or use 3.142 instead.

Here we are going to look at leaving answers in terms of

 Recap time.

Find the CIRCUMFERENCE of a this circle with a diameter of 6 cm. Leave your answer in terms of

The formula for finding the circumference of a circle is x diameter.

This is where the joy comes in no working out to do.  We know the diameter is 6 so we just write

circumference = 6π

 

Find the AREA of the circle with a radius of 3 cm

The formula for the area  of a circle = x radius x radius or  Πr²

Here all you have to do in find radius x radius and put after it.

3 x 3 = 9 so my answer is 9π

 

You may be asked to calculate something a bit different and leave your answer in terms of

 

For example, what is the length of the curve of this quarter circle.

You will have worked it all out and let's say you have an answer of 9.424777961.

To convert this into terms of Π just divide your answer by Π

It is best to use the Π button on your calculator as it will sometimes round it up for you.

Answers are usually shown to the nearest whole number.

So our answer here is 3Π

Any calculation you have to show in terms of Π  just divide by Π

 

pirate

Did you know that 3.142% of sailors are pi rates!!!

 

Find the circumference of this cake.

The diameter is 8 cm.

Leave your answer in terms of Π

C = 24π cm

C = 16π cm

C = 8π cm

C = 4π cm

Find the area of this coin.

The radius is 2 cm.

 

π8 cm²

π4 cm²

π16 cm²

π12 cm²

Match up

Column A

Column B

Circumference of a circle when diameter is 6 cm
49π cm²
Area of a circle with radius of 6 cm
12π cm
Circumference of a circle when diameter is 12 cm
24π cm
Circumference of a circle when diameter is 24 cm
6π cm
Area of a circle with radius of 8 cm
36π cm²
Area of a circle with diameter of 14 cm
64π cm²

 

This dartboard has a diameter of 44 cm.

Calculate the following.  Leave you answers in terms of &pi:

Column A

Column B

Circumference of a circle when diameter is 6 cm
49π cm²
Area of a circle with radius of 6 cm
12π cm
Circumference of a circle when diameter is 12 cm
24π cm
Circumference of a circle when diameter is 24 cm
6π cm
Area of a circle with radius of 8 cm
36π cm²
Area of a circle with diameter of 14 cm
64π cm²

Calculate the circumference and area of this table in terms of Π

The radius is 60 cm.

 60π cm30π cm120π cm3600π cm²360π cm²36π cm²
Circumference
Area

The area of this pond is 114 m²

What is its area in terms of Π

6Π cm²

36Π cm²

37&Pi cm²

6.6Π cm²

 

The circumference of this pizza is  37.7 cm.

What is the circumference in terms of π

37Π cm

24Π cm

15Π cm

12Π cm

Match up to the answers in terms of Π

Round to the nearest whole number,

 

Column A

Column B

Circumference 98 cm
31Π cm
Circumference 44 cm
17Π cm
Circumference 56 cm
14Π cm
Area 42 cm²
13Π cm²
Area 150 cm²
48Π cm²
Area 88 cm²
28Π cm²

 

The blue circle has a diameter of 12 cm and a the green circle has a diameter of 4 cm.

Answers have been rounded to 2 decimal places.

 37. 60cm37.70 cm12.57cm12.66 cm52.36 cm50. 27 cm25π16π
Circumference of the blue circle
Circumference of the the green circle
Total Circumference for both circles
Total circumference for both circles in terms of π

 

This crockery set has a plate with a radius of 15 cm and a saucer with a radius of 7 cm.

Answers have been rounded to 2 decimal places. Calculate the 

 620.12cm²706.95 cm²153.96 cm²155.65 cm²860.91 cm²680.91 cm²276π274Π
Area of the plate
Area of the saucer
Total Area of plate and saucer
Total area in terms of π
  • Question 1

Find the circumference of this cake.

The diameter is 8 cm.

Leave your answer in terms of Π

CORRECT ANSWER
C = 8π cm
EDDIE SAYS
Oh how nice, no working out to do. Take π and put the number for the diameter in front of it. It's just like having your cake and eating it. Circumference = 8π
  • Question 2

Find the area of this coin.

The radius is 2 cm.

 

CORRECT ANSWER
π4 cm²
EDDIE SAYS
The formula for finding area = π x r x r r x r = 4 so area = 4π How easy is that, no worries about 3.142 and very little working out. Bargain.
  • Question 3

Match up

CORRECT ANSWER

Column A

Column B

Circumference of a circle when di...
6π cm
Area of a circle with radius of 6...
36π cm²
Circumference of a circle when di...
12π cm
Circumference of a circle when di...
24π cm
Area of a circle with radius of 8...
64π cm²
Area of a circle with diameter of...
49π cm²
EDDIE SAYS
Hopefully you are now getting into the swing of things. Circumference is always diameter x Π e.g circumference = 6π Area just calculate the radius x radius first and put π after it. e.g 6 x 6 = 36 area = 36π Did you spot the sneaky one? Of course you did one area gave the diameter and you had to halve it to get the radius. No much gets past you.
  • Question 4

 

This dartboard has a diameter of 44 cm.

Calculate the following.  Leave you answers in terms of &pi:

CORRECT ANSWER
EDDIE SAYS
Once you know the diameter the rest is easy. Circumference = 44Π Area find the radius first 44 ÷ 2 = 22 22 x 22 = 484 Area = 484Π
  • Question 5

Calculate the circumference and area of this table in terms of Π

The radius is 60 cm.

CORRECT ANSWER
 60π cm30π cm120π cm3600π cm²360π cm²36π cm²
Circumference
Area
EDDIE SAYS
Did you spot it? Of course, you were given the radius and not the diameter. For the circumference you needed to double 60cm (120cm) For the Area 60 x 60 = 3600 It is always worth just stopping to write down formulas and see what information you are already given. Any information you are not given can be worked out like in this question. To get a diameter we double the radius.
  • Question 6

The area of this pond is 114 m²

What is its area in terms of Π

CORRECT ANSWER
36Π cm²
EDDIE SAYS
Now this is where the Π button on your calculator comes into its own. Answers in terms of Π are nearly always rounded to the nearest whole number. Some calculators do this automatically. If you are going to use 3.142 round up to the nearest whole number unless otherwise told. Divide your area by Π that is all there is to it. 114 ÷ Π = 36Π cm²
  • Question 7

 

The circumference of this pizza is  37.7 cm.

What is the circumference in terms of π

CORRECT ANSWER
12Π cm
EDDIE SAYS
You can't eat it until you have calculated the circumference. Simple just divide by &Pi. 37.7 ÷ π = 12π cm
  • Question 8

Match up to the answers in terms of Π

Round to the nearest whole number,

 

CORRECT ANSWER

Column A

Column B

Circumference 98 cm
31Π cm
Circumference 44 cm
14Π cm
Circumference 56 cm
17Π cm
Area 42 cm²
13Π cm²
Area 150 cm²
48Π cm²
Area 88 cm²
28Π cm²
EDDIE SAYS
If you have had to calculate something and convert the answer in terms of π this is the easy bit. All the hard work you have done before. Take your answer and divide by π Answers are usually given to the nearest whole number.
  • Question 9

 

The blue circle has a diameter of 12 cm and a the green circle has a diameter of 4 cm.

Answers have been rounded to 2 decimal places.

CORRECT ANSWER
 37. 60cm37.70 cm12.57cm12.66 cm52.36 cm50. 27 cm25π16π
Circumference of the blue circle
Circumference of the the green circle
Total Circumference for both circles
Total circumference for both circles in terms of π
EDDIE SAYS
Were you going around in circles? This is just a combination of your skill set so far. Circumference = π x diameter. Use this to find circumferences of both circles. Add together to get total circumference Divide by π to get total circumference in terms of π
  • Question 10

 

This crockery set has a plate with a radius of 15 cm and a saucer with a radius of 7 cm.

Answers have been rounded to 2 decimal places. Calculate the 

CORRECT ANSWER
 620.12cm²706.95 cm²153.96 cm²155.65 cm²860.91 cm²680.91 cm²276π274Π
Area of the plate
Area of the saucer
Total Area of plate and saucer
Total area in terms of π
EDDIE SAYS
Are you feeling pi eyed from all this? This is just a combination of your skill set so far. Area = π x r x r. Use this to find area of plate and saucer Add together to get total area Divide by π to get total area in terms of π I need a strong cup of tea after that.
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