Mathematics for IGCSE & O level - Similarity (Section 3)
1
Josh bought a set of table mats. The set contained mats of three different sizes. The smallest one was 5 cm by 8 cm, the middle one was an enlargement of the smallest by scale factor 3, and the shorter side of the largest mat was 25cm. Find the dimensions of the two larger mats.
Answer
(A)
15 cm by 24 cm and 75 cm by 120 cm
2
A model of a building is made to a scale of 1:50. If a room in the model has dimensions 7.4cm by 9.8cm by 6.5cm, calculate the actual volume
Answer
(D)
1710000 m³
3
Two rectangles are similar. The first rectangle is 2cm wide and 4cm long. The second rectangle is 4cm wide. What is the length of the second rectangle?
Answer
(C)
7 cm
4
If the volume scale factor is 216, what is the length scale factor?
Answer
(B)
6
5
Two similar containers hold 1 litre and 2 litres of milk. If the surface area of the larger container is 1100 cm², what is the surface area of the smaller one?
Answer
(B)
777.8 cm²
6
At noon a radio mast of height 12m has a shadow length of 16m. Calculate the height of a tower with a shadow length of 56m at noon.
Answer
(B)
42 m
7
The volume scale factor is 216. What is the length scale factor?
Answer
(B)
6
8
A glass holds 15 cl. How tall is a similar glass that holds twice as much?
Answer
(A)
15 * 2^(1/3) cl
9
If the height of a cone is doubled, by what factor is the volume increased?
Answer
(B)
4
10
A model aircraft is made to a scale of 1:50. The area of the wing on the model is 18 cm². What is the area of the wing on the real aircraft?
Answer
(D)
450000 cm²
11
What must be true for two shapes to be similar?
Answer
B
C
12
The heights of two similar glasses are in the ratio 1:1.2. How do you calculate the capacity of the larger glass?
Answer
(C)
Multiply the capacity of the smaller glass by 1.728
