13 marks
Two solid ornaments, P and Q, are mathematically similar.
P has height 4 cm and Q has height 12 cm.
The volume of P is 20 cm3.
Work out the volume of Q.
Show answer
540 cm³
Similar shapes: areas and volumes
Squared and cubed scale factors.
11 original questions, 41 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
The questions
23 marks
Two mathematically similar signs are made for a shop.
The small sign is 5 cm wide and has area 50 cm2.
The large sign is 8 cm wide.
Work out the area of the large sign.
Show answer
128 cm²
34 marks
A shop sells two mathematically similar tins of paint. The small tin is 12 cm tall and holds 0.8 litres. The large tin is 18 cm tall.
- Work out the capacity of the large tin.
- The small tin costs £5.60. The price of paint is the same per litre for both tins. Work out the cost of the large tin.
Show answer
a) 2.7 litres b) £18.90
43 marks
Two mathematically similar solids, A and B, have volumes in the ratio 64 : 343.
Find the ratio of the surface area of A to the surface area of B.
Give your answer in its simplest form.
Show answer
16 : 49
53 marks
Two mathematically similar candles, C and D, are made from the same wax.
C has surface area 36 cm2 and D has surface area 81 cm2.
The volume of C is 24 cm3.
Work out the volume of D.
Show answer
81 cm³
64 marks
Two mathematically similar statues are to be painted.
The small statue has height 10 cm and surface area 80 cm2.
The large statue has height 25 cm.
Work out the surface area of the large statue.
Show answer
500 cm²
74 marks
Two solid trophies are mathematically similar and are made from the same metal.
The small trophy has height 6 cm and mass 120 g.
The large trophy has height 9 cm.
Work out the mass of the large trophy.
Show answer
405 g
84 marks
Two mathematically similar bottles hold 250 ml and 686 ml of juice when full.
The small bottle has height 15 cm.
Work out the height of the large bottle.
Show answer
21 cm
94 marks
Two mathematically similar solids, S and T, have volumes 135 cm3 and 320 cm3.
The surface area of S is 180 cm2.
Work out the surface area of T.
Show answer
320 cm²
104 marks
In triangle ABC, D lies on AB and E lies on AC so that DE is parallel to BC.
AD : DB = 2 : 1.
The area of triangle ADE is 24 cm2.
Work out the area of the trapezium DBCE.
Show answer
30 cm²
115 marks
Two mathematically similar containers, A and B, have volumes 400 cm3 and 1350 cm3.
- Container A has height 12 cm. Work out the height of container B.
- Container B has surface area 468 cm2. Work out the surface area of container A.
Show answer
a) 18 cm b) 208 cm²
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.
All Grade 7 topics
- Simplifying surds
- Fractional indices
- Factorising quadratics (ax^2 + bx + c)
- Completing the square
- Perpendicular lines
- Algebraic fractions
- Rearranging formulae where the subject appears twice
- nth term of a quadratic sequence
- Algebraic proof
- Exponential graphs
- Composite and inverse functions
- Inverse proportion equations
- Sine rule
- Cosine rule
- Area of a triangle using 1/2 ab sin C
- Circle theorems
- Similar shapes: areas and volumes
- Conditional probability with Venn diagrams
- Histograms with unequal class widths
- Capture-recapture sampling
- Mean from a histogram