Grade DE Compare lengths areas volumes Compare lengths

Grade D/E Compare lengths, areas, volumes Compare lengths, areas, and volumes using ratio notation If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Length Area Volume Scale factor Enlarge Reduce

How to compare lengths, areas, volumes 1) Share £ 42 into the ratio 1 : 5 We add the parts of the ratio 1+5=6 To find each part, we divide £ 42 by 6 42 ÷ 6 = £ 7 This means one part is equivalent to £ 7 Since one gets 1 part = 1 x £ 7 = £ 7 Since the other gets 5 parts = 5 x £ 7 = £ 35 How can you check your answer?

How to compare lengths, areas, volumes 2) Below shape is enlarged by scale factor of 3 Write down the new width and length. 6 cm New width = 6 x 3 = 18 cm 12 cm New length = 12 x 3 = 36 cm

How to compare lengths, areas, volumes 3) The triangle below is enlarged by scale factor of 2. Write down the area of the new triangle. 5 cm 8 cm Area of the triangle = (8 x 5)/2 = 20 cm 2 Area factor = 2 x 2 New area = 20 x 4 = 80 cm 2

How to compare lengths, areas, volumes 4) The rectangle below is enlarged by scale factor of 4. Write down the area of the new rectangle. 6 cm 10 cm Area of the rectangle = 10 x 6 = 60 cm 2 Area factor = 4 x 4 New area = 60 x 16 = 960 cm 2

How to compare lengths, areas, volumes 5) A cuboid has volume of 80 cm 3. If it is enlarged by scale factor of 3. Calculate the volume of the new cuboid. Volume of the cuboid = 80 cm 3 Volume factor = 3 x 3 New volume = 80 x 27 = 2160 cm 3 Do we always have to enlarge?

How to compare lengths, areas, volumes – Now you try … 1) A rectangle is 14 cm long and 7 cm wide. It is enlarged by scale factor of 3. Find the new length and width. 2) Shape A has area of 15 cm 2. Shape B is an enlargement of shape A by scale factor of 2. Find the area of shape B. 3) The cube below is enlarged by scale factor of 3. Find the volume of the enlarged cube. 4 cm

How to compare lengths, areas, volumes – Now you try … 1) A rectangle is 14 cm long and 7 cm wide. It is enlarged by scale factor of 3. Find the new length and width. 1) length = 42 cm, width = 21 cm 2) Shape A has area of 15 cm 2. Shape B is an enlargement of shape A by scale factor of 2. Find the area of shape B. 2) 60 cm 2 3) The cube below is enlarged by scale factor of 3. Find the volume of the enlarged cube. 3) 1728 m 3 4 m

Problem Solving and Reasoning B A Shape A has area of 20 m 2. Shape B has an area of 320 m 2. Find the scale factor. 320 ÷ 20 = 16 Scale factor squared = 16 Scale factor is => √ 16 = 4

Problem Solving and Reasoning B A Cube A has volume of 216 cm 3. Cube B has volume of 729 m 2. Find the scale factor and area of cube B. 729 ÷ 216 = 3. 375 Scale factor cubed = 3. 375 3 Scale factor is => √ 3. 375 = 1. 5

Problem Solving and Reasoning A B Circle A has area of 20 m 2. Circle B is an enlargement of circle A by scale factor of 3. Find the radius of B. Circle A area => 20 m 2 Scale factor 3 for area means => 3 x 3 = 9 Circle B area => 20 x 9 = 180 m 2 Circle B area = 180 m 2 Πr 2 = 180 r 2 = 57. 3 => r = 7. 6 m

Reason and explain True or false: A 6 cm • • • 8 cm B 9 cm A is enlargement of B. Scale factor is 1. 5 Width of B is 11 cm Area of B is 3 times the area of A. Perimeter of B is 1. 5 x 1. 5 times the perimeter of A. We can fit 48 2 x 2 squares into shape A.