# Similar Shapes

## Questions about the scale factors of lengths, areas and volumes of similar shapes.

##### Level 1Level 2Level 3Level 4Level 5DescriptionHelpEnlargements

This is level 4; Mixed questions. You can earn a trophy if you get at least 7 questions correct.

 A photograph is 17cm long. It is enlarged by a scale factor of two. How long will the enlargement be? Working: cm The statue of a cat is 245cm tall which is seven times bigger than the actual cat which was used as the model. How tall is the real cat? Working: cm A rectangle has an area of 17cm2. A second rectangle is similar to the first but its dimensions are three times bigger. What is the area of the second rectangle? Working: cm2 A box has a surface area of 486cm2. A second box is 2 times as wide,2 times as long and 2 times as tall. What is the surface area of the second box? Working: cm2 The smaller box shown above has a volume of 729cm3. What is the volume of the second box given that its dimensions are twice the first box's? Working: cm3 The volume of a large bottle of wine is 2700ml. A minature bottle is similar to the large bottle but its dimensions are three times smaller. What is the volume of the smaller bottle? Working: ml The area of a piece of land is 53.76m2. The same piece of land is shown on a map by an area of 21cm2. How long would a footpath be if on the map it is 13cm long? Working: m A real bus is eighteen times as long as a model which was used in the design process. All of the other dimensions are in proportion. The area of the glass in the windows of the model is 1m2. What is the area of the glass in the real bus? Working: m2 The capacity of the fuel tank of the real bus mentioned above is 116640cc. What is the capacity of the fuel tank on the model? Working: cc The model bus has five tyres (including the spare). How many tyres does the real bus have? Working: tyres
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This is Similar Shapes level 4. You can also try:
Level 1 Level 2 Level 3 Level 5

## 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.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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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 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

#### Roman Numerals Jigsaw

This is a wonderful activity for someone who does not know Roman numerals. By completing the activity an understanding of the symbols develops and a great sense of achievement is enjoyed.

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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.

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## 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:

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## Description of Levels

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Level 1 - Lengths of similar shapes

Level 2 - Areas of similar shapes

Level 3 - Volumes of similar shapes

Level 4 - Mixed questions

Level 5 - Exam-style questions

## Enlargements

If you enlarge the dimensions of a polygon by multiplying them by a number (scale factor), the area is increased by the square of that factor.

For example if the sides of a rectangle are enlarged by a factor of 6, the area of the rectangle increases by a factor of 62

If the length of the original rectangle was 5cm and the width was 2cm then after enlargement they would be 30cm and 12cm respectively.

The area of the original rectangle is 5cm x 2cm = 10cm2

The area of the enlarged rectangle is 30cm x 12cm = 360cm2

As you can see the area of the enlarged rectangle is 62 times larger than the area of the original rectangle.

The same can be shown for any polygon when enlarged.

Enlargement by a fractional scale factor is equivalent to the shape reducing in size.

If you enlarge the dimensions of a three dimensional shape by a scale factor, the volume is increased by the cube of that factor.

For example if the sides of a cuboid are enlarged by a factor of 6, the volume of the cuboid increases by a factor of 63

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