Mathematics for IGCSE & O level - Similarity (Section 2)
1
If the height of a triangle is doubled while the base remains constant, what is the effect on the area?
Answer
(A)
The area doubles.
2
Two triangles ABC and BDC, where angle ABC = angle BDC = 90° and AB=6cm, BC=8cm, and BD=4.8cm. What is the length of DC?
Answer
(B)
6.4 cm
3
The scale on a map is 1:50,000. If two cities are 3 cm apart on the map, what is the actual distance in kilometers?
Answer
(B)
1.5 km
4
A glass holds 15 cl. If the capacity is doubled, how does the height change?
Answer
(C)
multiplied by ∛2
5
A cube has a surface area of 54 cm². If each side is doubled, what is the new surface area?
Answer
(D)
432 cm²
6
If two similar figures have a surface area ratio of 49:81, what is the ratio of their corresponding side lengths?
Answer
(A)
7:9
7
If the sides of a square are tripled, what is the change in the area?
Answer
(C)
Area is multiplied by 9
8
If the area of a square is doubled, what is the effect on the side length?
Answer
(B)
The side length is multiplied by √2.
9
If the volume of a cube is 64 cm³, and a similar cube has a side length that is twice as long, what is the volume of the larger cube?
Answer
(D)
512 cm³
10
A small sphere has a radius of 3 cm. A larger sphere has a radius of 9 cm. By what factor has the surface area of the sphere increased?
Answer
(C)
9
11
A model of a building has a volume of 1000 cm³. The actual building is built to a scale of 1:100. What is the volume of the actual building?
Answer
(D)
10000000000 cm³
12
A glass holds 15 cl, and a larger similar glass is in the ratio 1:1.2. Calculate the capacity of the larger glass.
Answer
(C)
25.92 cl
13
The ratio of the volumes of two similar cones is 8:27. What is the ratio of their heights?
Answer
(A)
2:3
14
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
15
A model building has a height of 10 cm. The actual building is 50 m tall. What is the scale used to build the model?
Answer
(B)
1:50
16
The model has a volume of 1340 cm³. What will be the volume of the sculpture if the scale factor is 10?
Answer
(D)
1340000 cm³
17
Two similar cones have heights in a ratio of 2:5. If the surface area of the smaller cone is 24 cm², what is the surface area of the larger cone?
Answer
(D)
24 cm²
18
If the scale factor between two similar figures is 1:0.5, what is the ratio of their areas?
Answer
(A)
1:0.25
19
Two similar figures have a volume ratio of 64:125. What is the ratio of their corresponding side lengths?
Answer
(A)
4:5
20
A model of a building is made to a scale of 1:50. A room in the model is a cuboid with dimensions 7.4cm by 9.8cm by 6.5cm high. Calculate the floor area of the room in the actual building.
Answer
(D)
181.3 m²
21
A tray has an area of 160 cm². What is the area of a similar tray if the lengths are halved?
Answer
(A)
40 cm²
22
The rectangles ABCD and PQRS are similar. Find the length of PQ if AB=6cm, CD=4cm, and BC=5cm.
Answer
(A)
7.5 cm
23
A model aircraft is made to a scale of 1:48. The area of the wing of the real aircraft is 52 m². What is the area of the wing of the model?
Answer
(A)
0.0226 m²
24
Three similar wooden boxes have heights in the ratio 3:4:5. What is the ratio of their volumes?
Answer
(C)
27:64:125
25
Three similar wooden boxes have heights in the ratio 3:4:5. What is the ratio of their volumes?
Answer
(C)
27:64:125
26
A jug holds 50cl is 12 cm high. A similar jug holds 2 litres. What is its height?
Answer
(A)
19.0 cm
27
A tray has an area of 169 cm². What is the area of a similar tray whose lengths are one and a half times as large?
Answer
(B)
380.25 cm²
28
The length scale factor is 10. What is the area scale factor?
Answer
(C)
100
29
The area of a rug is 2.4 times as large as the area of a similar rug. If the length of the smaller rug is 1.6m, find the length of the larger rug.
Answer
(A)
2.47m
30
If a model drawn an area of 5m² in real life is represented by 20 cm² on the model, what is the scale?
Answer
(C)
1:50
31
The heights of two similar glasses are in the ratio 1:1.2. Calculate the capacity of the larger glass.
Answer
(C)
1.728 times the smaller
32
A model of a building is made to a scale of 1:50. A room in the model has dimensions 7.4cm by 9.8cm by 6.5cm. Calculate the floor area of the room in the actual building.
Answer
(D)
18.13 m²
33
If two rectangles are similar, and the scale factor of the sides is 3, how does the area change?
Answer
(D)
Increases by a factor of 9
34
The lengths of the sides of a rectangle are doubled. By what factor is the area increased?
Answer
(C)
4
35
The area of a rug is 2.4 times as large as the area of a similar rug. What is the length of the larger rug if the length of the smaller rug is 1.6m?
Answer
(A)
2.47 m
36
The area of a square is 4 cm². If the square is enlarged by increasing the length of its sides by 100%, what will be the area of the enlarged square?
Answer
(C)
16 cm²
37
If a cube has a volume of 8 cm³ and it is enlarged by a scale factor of 2, what is the new volume?
Answer
(D)
64 cm³
38
The surface area of a container is 100 cm². If the container is enlarged with a length scale factor of 3, what will be the new surface area?
Answer
(C)
900 cm²
39
To what scale is a model drawn if an area of 5 m² in real life is represented by 20 cm² on the model?
Answer
(B)
1:100
40
An artist makes a model for a large sculpture. The model is 24cm high. The finished sculpture will be 3.6m high. Find the length scale factor.
Answer
(A)
15
41
In the triangle, angle ABC = angle BDC = 90°, AB = 6 cm, BC = 8 cm and BD = 4.8 cm. What is the length of DC?
Answer
(B)
6.4 cm
42
The area of a rug is 2.4 times as large as the area of a similar rug. If the length of the smaller rug is 1.6m, find the length of the larger rug.
Answer
(B)
2.4 m
43
A tray has an area of 169 cm². What is the area of a similar tray whose lengths are one and a half times as large?
Answer
(B)
380.25 cm²
44
If two shapes are similar, what must be true about their corresponding angles?
Answer
(B)
They must be equal.
45
In mathematics, what does the word 'similar' mean?
Answer
(C)
Exact enlargement of the other
46
A cube has a volume of 10 cm³. If the cube's side lengths are tripled, what is the new volume?
Answer
(C)
270 cm³
47
If a model of a building is created to a scale of 1:50, and a room in the model has dimensions 7.4 cm by 9.8 cm by 6.5 cm, calculate the floor area of the room in the actual building.
Answer
(D)
18.5 m²
48
If the length scale factor is 2, what is the area scale factor?
Answer
(B)
4
49
For two shapes to be similar, which conditions must be met?
