Similar Shapes (Area and Volume): Fluency and Exam Drill - Worksheets, Questions and Revision

22 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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6.8D Similar Shapes (Area and Volume): Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 70 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Two mathematically similar shapes have a linear scale factor of 3 from the smaller shape to the larger shape. The area of the smaller shape is 8 cm2. Work out the area of the larger shape.
(Total for Question 1 is 2 marks)
2
Two mathematically similar shapes have a linear scale factor of 5 from the smaller shape to the larger shape. The area of the smaller shape is 6 cm2. Work out the area of the larger shape.
(Total for Question 2 is 2 marks)
3
Two mathematically similar solids have a linear scale factor of 2 from the smaller solid to the larger solid. The volume of the smaller solid is 20 cm3. Work out the volume of the larger solid.
(Total for Question 3 is 2 marks)
4
Two mathematically similar solids have a linear scale factor of 4 from the smaller solid to the larger solid. The volume of the smaller solid is 3 cm3. Work out the volume of the larger solid.
(Total for Question 4 is 2 marks)
5
Two mathematically similar shapes have areas of 18 cm2 and 72 cm2. Find the linear scale factor from the smaller shape to the larger shape.
(Total for Question 5 is 2 marks)
6
Two mathematically similar shapes have areas of 20 cm2 and 45 cm2. Find the linear scale factor from the smaller shape to the larger shape.
(Total for Question 6 is 2 marks)
7
Two mathematically similar solids have volumes of 8 cm3 and 64 cm3. Find the linear scale factor from the smaller solid to the larger solid.
(Total for Question 7 is 2 marks)
8
Two mathematically similar solids have volumes of 12 cm3 and 40.5 cm3. Find the linear scale factor from the smaller solid to the larger solid.
(Total for Question 8 is 2 marks)
9
The linear scale factor between two mathematically similar solids is 2.5. Work out the volume scale factor.
(Total for Question 9 is 2 marks)
10
The linear scale factor between two mathematically similar shapes is 0.4. Work out the area scale factor.
(Total for Question 10 is 2 marks)
11
A scale model of a bus is built using a linear scale factor of 1/20 from the real bus to the model. Work out the volume scale factor from the real bus to the model.
(Total for Question 11 is 2 marks)
12
Two mathematically similar triangles have corresponding sides in the ratio 3:7. Find the ratio of their areas.
(Total for Question 12 is 2 marks)
13
Two mathematically similar spheres have radii in the ratio 2:5. Find the ratio of their volumes.
(Total for Question 13 is 2 marks)
14
Two mathematically similar shapes have perimeters in the ratio 4:9. Find the ratio of their areas.
(Total for Question 14 is 2 marks)
15
Amara is designing two mathematically similar circular garden ponds. Pond A has a diameter of 2 m and a surface area of 6 m2. Pond B has a diameter of 5 m. Work out the surface area of pond B.
(Total for Question 15 is 3 marks)
16
Jar A and jar B are mathematically similar storage jars. Jar A has a height of 12 cm and a volume of 480 cm3. Jar B has a height of 18 cm. Work out the volume of jar B.
(Total for Question 16 is 3 marks)
17
Owen collects rainwater in two mathematically similar water butts. The curved surface area of the small water butt is 150 cm2 and the curved surface area of the large water butt is 486 cm2. The volume of the small water butt is 250 cm3. Work out the volume of the large water butt.
(Total for Question 17 is 4 marks)
18
Two mathematically similar trophies are made from the same solid metal, so mass is proportional to volume. The height of the smaller trophy is 15 cm and its mass is 2.4 kg. The height of the larger trophy is 22.5 cm.
(a)Work out the mass of the larger trophy.(3)
(b)A gold-effect coating is applied to the surface of each trophy. The surface area of the smaller trophy is 340 cm2. Explain, with a calculation, whether the amount of coating needed for the larger trophy is more than double the amount needed for the smaller trophy.(2)
(Total for Question 18 is 5 marks)
19
Rhys runs a pet shop with two mathematically similar aquarium tanks, tank A and tank B. Tank A holds 64 litres and tank B holds 216 litres. Tank A has a height of 40 cm and a rectangular base of area 800 cm2.
(a)Find the linear scale factor from tank A to tank B.(2)
(b)Work out the height of tank B.(1)
(c)Work out the area of the base of tank B.(2)
(Total for Question 19 is 5 marks)
20
Funnel P and funnel Q are mathematically similar. The volumes of funnel P and funnel Q are in the ratio 27:1000. The slant height of funnel P is 9 cm. Work out the slant height of funnel Q.
(Total for Question 20 is 3 marks)
21
Block C and block D are mathematically similar solid blocks. A dimension of block C is (x + 3) cm and the corresponding dimension of block D is (4x - 6) cm. The volume scale factor from block C to block D is 8.
(a)Work out the value of x.(3)
(b)The volume of block C is 54 cm3. Work out the volume of block D.(2)
(Total for Question 21 is 5 marks)
22
Cylinder A and cylinder B are mathematically similar. The ratio of their curved surface areas is 4:9. The volume of cylinder A is 32 cm3. Show that the volume of cylinder B is 108 cm3.
(Total for Question 22 is 3 marks)
Mark scheme · 6.8D Similar Shapes (Area and Volume): Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22