# Similar Shapes

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

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

 1. The statue of a cat is 123cm tall which is three times bigger than the actual cat which was used as the model. How tall is the real cat? Working: cm 2. A rectangle has an area of 20cm2. 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 3. A box has a surface area of 600cm2. 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 4. The smaller box shown above has a volume of 1000cm3. What is the volume of the second box given that its dimensions are twice the first box's? Working: cm3 5. The volume of a large bottle of wine is 6400ml. A minature bottle is similar to the large bottle but its dimensions are four times smaller. What is the volume of the smaller bottle? Working: ml 6. The area of a piece of land is 101.08m2. The same piece of land is shown on a map by an area of 28cm2. How long would a footpath be if on the map it is 11cm long? Working: m 7. A real bus is seventeen 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 2m2. What is the area of the glass in the real bus? Working: m2 8. The capacity of the fuel tank of the real bus mentioned above is 88434cc. What is the capacity of the fuel tank on the model? Working: cc 9. The model bus has five tyres (including the spare). How many tyres does the real bus have? Working: tyres 10. In a triangle ABC, D is a point on the line AC and E is a point on the line AB. A straight line connects D and E and is parallel to CB. Sketch the diagram and mark the following lengths:DE is 4cm,AE is 1cm longer than DE,DC is 1cm shorter than DE,CB is 4cm longer than DC.The two triangles in the diagram are similar. What is area of the larger triangle (to the nearest whole number of square centimetres) if the area of the smaller triangle is 7.81cm2? Working: cm2
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This is Similar Shapes level 4. You can also try:
Level 1 Level 2 Level 3

## Instructions

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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

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

Similar Parts Puzzle - Use the colours to dissect the outlines into similar parts.

More on Enlargements including lesson Starters, visual aids, investigations and self-marking exercises.

Square in Rectangle - An advanced lesson Starter.

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## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## 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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