1. 1
   Two similar containers have a linear scale factor of 3 : 1 (larger to smaller). The smaller container holds 2 litres.

   (a)

   What is the ratio of the surface areas (larger : smaller)?

   [1 mark]

   • A9 : 1
   • B3 : 1
   • C27 : 1
   • D6 : 1

   (b)

   What is the ratio of the volumes (larger : smaller)?

   [1 mark]

   • A18 : 1
   • B9 : 1
   • C3 : 1
   • D27 : 1

   (c)

   How many litres does the larger container hold?

   [1 mark]

   • A18 litres
   • B54 litres
   • C6 litres
   • D27 litres

   Total for question 1: 3 marks

2. 2
   Two similar triangles have areas 18 cm² (smaller) and 50 cm² (larger). A side of the larger triangle has length 15 cm.

   (a)

   Find the ratio of the lengths (linear scale factor) between the smaller and larger triangle.

   [2 marks]

   (b)

   Find the length of the corresponding side in the smaller triangle.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two similar statues are made from the same material and have the same density. Their heights are 40 cm (smaller) and 60 cm (larger). The smaller statue has a mass of 5 kg.

   (a)

   Find the ratio of the surface areas of the two statues (smaller : larger).

   [3 marks]

   (b)

   Find the mass of the larger statue, giving your answer to 3 significant figures.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Two mathematically similar water tanks are shaped like cones. The volume of the smaller tank is 250 litres and the volume of the larger tank is 2000 litres. The smaller tank requires 3 m² of material to construct. Material costs 45 dollars per m², plus a fixed fee of 20 dollars to cut the material to shape (charged once per tank, regardless of size).

   (a)

   Find the linear scale factor from the smaller tank to the larger tank.

   [4 marks]

   (b)

   Using your answer to part (a), find how much material, in m², the larger tank requires.

   [4 marks]

   (c)

   Find the total cost of material for the larger tank, and state whether the total cost is exactly 4 times the cost for the smaller tank. Justify your answer.

   [5 marks]

   Total for question 4: 13 marks

End of questions