Similar Shapes (Area and Volume) - Worksheets, Questions and Revision

20 original exam-style questions - 11 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 12)Read the revision guide
« Previous: Inequalities on GraphsNext: Similar Shapes (Area and Volume): Fluency and Exam Drill »
Revision Library
revisionlibrary.co.uk
HIGHER

6.8 Similar Shapes (Area and Volume)

EDEXCEL 1MA1 · Calculator allowed · about 100 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Triangle PQR is mathematically similar to triangle STU, where P corresponds to S, Q corresponds to T and R corresponds to U.
P Q R S T U
(a)Write down the relationship between angle P and angle S.(1)
(b)Write down the relationship between the ratio PQ:ST and the ratio QR:TU.(1)
(Total for Question 1 is 2 marks)
2
Rectangle A and rectangle B are mathematically similar. Rectangle A has length 8 cm and width 5 cm. Rectangle B has length 20 cm.
Diagram NOT accurately drawn
8 cm 5 cm Rectangle A 20 cm w cm Rectangle B
(a)Work out the scale factor of the enlargement from rectangle A to rectangle B.(1)
(b)Work out the width of rectangle B.(2)
(Total for Question 2 is 3 marks)
3
Shape A is enlarged by scale factor 3 to give mathematically similar shape B.
(a)Circle the correct statement.(1)
  • A) Area of B = 3 x Area of A
  • B) Area of B = 9 x Area of A
  • C) Area of B = 6 x Area of A
  • D) Area of B = 27 x Area of A
(Total for Question 3 is 1 mark)
4
Triangle ABC is mathematically similar to triangle XYZ, where A corresponds to X, B corresponds to Y and C corresponds to Z. AB = 9 cm, BC = 12 cm and AC = 15 cm. XY = 15 cm.
Diagram NOT accurately drawn
A B C AB = 9 cm BC = 12 cm AC = 15 cm X Y Z XY = 15 cm
(a)Calculate the length of YZ.(2)
(b)Calculate the length of XZ.(1)
(Total for Question 4 is 3 marks)
5
Shape P and shape Q are mathematically similar. The linear scale factor from shape P to shape Q is 4. The area of shape P is 15 cm2.
(a)Work out the area scale factor from shape P to shape Q.(1)
(b)Work out the area of shape Q.(2)
(Total for Question 5 is 3 marks)
6
Solid A and solid B are mathematically similar. The linear scale factor from solid A to solid B is 1.5. The volume of solid A is 40 cm3.
(Total for Question 6 is 3 marks)
7
Rectangle R and rectangle S are mathematically similar. Rectangle R measures 4 cm by 7 cm. Rectangle S measures 10 cm by 17.5 cm.
Diagram NOT accurately drawn
4 cm 7 cm R 10 cm 17.5 cm S
(Total for Question 7 is 3 marks)
8
Shape C and shape D are mathematically similar. The area of shape C is 18 cm2 and the area of shape D is 50 cm2. A side of shape C is 6 cm.
(a)Work out the linear scale factor from shape C to shape D.(2)
(b)Work out the length of the corresponding side on shape D.(2)
(Total for Question 8 is 4 marks)
9
Solid E and solid F are mathematically similar. The volume of solid E is 64 cm3 and the volume of solid F is 216 cm3. The height of solid E is 8 cm.
(a)Work out the linear scale factor from solid E to solid F.(2)
(b)Work out the height of solid F.(2)
(Total for Question 9 is 4 marks)
10
A cylindrical tin of paint has height 12 cm. Coating the curved surface area of the tin uses 250 ml of paint. A mathematically similar cylindrical tin has height 18 cm. The amount of paint needed is proportional to the curved surface area of the tin.
Diagram NOT accurately drawn
12 cm 18 cm
(Total for Question 10 is 4 marks)
11
Cone G and cone H are mathematically similar. The base radius of cone G is 5 cm and the base radius of cone H is 8 cm. The surface area of cone G is 130 cm2 and the volume of cone G is 150 cm3.
Diagram NOT accurately drawn
G 5 cm H 8 cm
(a)Work out the surface area of cone H.(3)
(b)Work out the volume of cone H.(2)
(Total for Question 11 is 5 marks)
12
A model car is built using a scale of 1:24 compared with the real car (every linear dimension of the real car is 24 times the corresponding dimension of the model). The model car has a volume of 90 cm3 and a surface area of 220 cm2.
(a)Work out the volume of the real car. Give your answer in cm3, in standard form correct to 3 significant figures.(3)
(b)Work out the surface area of the real car in m2, correct to 3 significant figures.(3)
(Total for Question 12 is 6 marks)
13
Two solid bronze statues are mathematically similar. The height of the smaller statue is 30 cm and its mass is 12 kg. The height of the larger statue is 45 cm. The statues are made from the same bronze, so mass is proportional to volume.
(Total for Question 13 is 4 marks)
14
Container J and container K are mathematically similar. The surface area of container J is 96 cm2 and the surface area of container K is 216 cm2. The volume of container J is 64 cm3.
(Total for Question 14 is 4 marks)
15
The length of every edge of a solid shape is increased by 40% to make a similar, larger solid.
(a)Work out the percentage increase in the surface area of the solid.(2)
(b)Work out the percentage increase in the volume of the solid.(2)
(Total for Question 15 is 4 marks)
16
Shape M and shape N are mathematically similar. A side of shape M has length (x + 2) cm. The corresponding side of shape N has length (3x - 4) cm. The area scale factor from shape M to shape N is 4.
(Total for Question 16 is 3 marks)
17
Vase P and vase Q are mathematically similar. The volume of vase P is 250 cm3 and the volume of vase Q is 500 cm3. The height of vase P is 18 cm.
(Total for Question 17 is 4 marks)
18
A cone has height 24 cm. It is cut by a plane parallel to the base, 8 cm from the vertex, forming a smaller cone (mathematically similar to the original cone) and a frustum. The whole cone has volume 900 cm3.
Diagram NOT accurately drawn
24 cm 8 cm small cone frustum
(a)Work out the ratio of the volume of the small cone to the volume of the frustum. Give your answer in the form 1 : n.(3)
(b)Work out the volume of the frustum.(2)
(Total for Question 18 is 5 marks)
19
A company sells two mathematically similar spherical balloons. The small balloon has diameter 20 cm and costs 3.50 pounds. The large balloon has diameter 35 cm and costs 9.50 pounds. The company intends the cost of each balloon to be proportional to the amount of material used to make it (its surface area).
(a)Work out the surface area scale factor from the small balloon to the large balloon.(2)
(b)Use your answer to part (a) to work out what the large balloon should cost if the cost is exactly proportional to surface area.(2)
(c)The large balloon actually costs 9.50 pounds. Comment on whether the large balloon is good value for money compared with the small balloon, giving a reason.(1)
(Total for Question 19 is 5 marks)
20
Two mathematically similar solid glass ornaments are made from the same type of glass, so mass is proportional to volume. Ornament A has volume 45 cm3 and mass 117 g. Ornament B has mass 351 g. The height of ornament A is 6 cm.
(a)Work out the volume of ornament B.(2)
(b)Work out the height of ornament B, giving your answer correct to 3 significant figures.(3)
(Total for Question 20 is 5 marks)
Mark scheme · 6.8 Similar Shapes (Area and Volume)

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