Mathematics for IGCSE & O level - Similarity (Section 1)
1
If the length scale factor between two similar figures is 4, what is the area scale factor?
Answer
(C)
16
2
In two similar triangles, one has a base of 10 cm and a height of 5 cm. If the corresponding base of the other triangle is 15 cm, what is its height?
Answer
(B)
10 cm
3
A square is enlarged by increasing the length of its sides by 10%. What is the area of the enlarged square if the length of the sides was originally 8 cm?
Answer
(B)
77.44 cm²
4
The area of a circle is 100π cm². If we scale the radius by a factor of 2, what is the new area?
Answer
(D)
800π cm²
5
Three similar wooden boxes have heights in the ratio 3:4:5. What is the ratio of their volumes?
Answer
(B)
27:64:125
6
What happens to the surface area of a sphere when its radius is multiplied by 4?
Answer
(C)
The area is 16 times larger.
7
If the surface area of a sphere is 100 cm², what would be the surface area of a similar sphere with a linear dimension three times as large?
Answer
(C)
900 cm²
8
A model rocket is 1/10 the size of the actual rocket. If the surface area of the model is 50 cm², what is the surface area of the actual rocket?
Answer
(D)
5000 cm²
9
If the ratio of the sides of two similar figures is 2:5, what is the ratio of their areas?
Answer
(C)
4:25
10
If the area of a circle increases by a factor of 9, by what factor has the radius increased?
Answer
(A)
3
11
What scale is a model drawn if an area of 5 m² in real life is represented by 20 cm² on the model?
Answer
(D)
1:500
12
A map has a scale of 1:25000. If the distance between two points on the map is 4 cm, what is the actual distance in kilometers?
Answer
(A)
0.1 km
13
A tray has an area of 160 cm². What is the area of a similar tray whose lengths are one and a half times as large?
Answer
(C)
1440 cm²
14
If a solid has a volume of 120 cm³ and is scaled by a factor of 1/3, what is the new volume?
Answer
(B)
40 cm³
15
What is the volume scale factor if the area scale factor is 9?
Answer
(C)
27
16
State the volume scale factor for a length scale factor of 4.
Answer
(B)
64
17
If a photograph is enlarged so that the length of each side is tripled, by what factor is the area increased?
Answer
(C)
9
18
Two shapes are similar, and the ratio of their areas is 16:9. What is the ratio of their perimeters?
Answer
(A)
4:3
19
A model of a car is made to a scale of 1:20. If the surface area of the real car is 10 m², what is the surface area of the model?
Answer
(A)
0.025 m²
20
A jug holding 50 cl is 12 cm high. A similar jug holds 2 liters. What is the height of the larger jug?
Answer
(B)
19.0 cm
21
If the sides of a triangle are increased by a factor of 4, by what factor is the area increased?
Answer
(D)
16
22
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
(C)
1100 cm²
23
If the volume of a box is 24 cm³ and a similar box has sides that are twice as long, what is the volume of the larger box?
Answer
(B)
72 cm³
24
The lengths of the sides of a triangle are in the ratio 2:3:4. If the smallest side of a similar triangle is 6cm, what is the length of the longest side?
Answer
(B)
12 cm
25
In mathematics, what does the word 'similar' mean?
Answer
(C)
An exact enlargement of the other
26
A building casts a shadow of 20 m at the same time as a 1 m ruler casts a shadow of 0.5 m. What is the height of the building?
Answer
(D)
50 m
27
Two similar containers hold 1 litre and 2 litres of milk. If the surface area of the larger container is 1100 cm², calculate the surface area of the smaller one.
Answer
(C)
693 cm²
28
The volumes of two similar solids are in the ratio 1:8. What is the ratio of their surface areas?
Answer
(B)
1:4
29
A radio mast of height 12m has a shadow length of 16m. Calculate the height of a tower with a shadow length of 56m.
Answer
(C)
48 m
30
A model car is built to a scale of 1:50. The volume of the real car's trunk is 2 m³. What is the volume of the trunk in the model?
Answer
(B)
0.0008 m³
31
A model aircraft is made to a scale of 1:48. If the area of the wing of the real aircraft is 52 m², what is the area of the wing on the model?
Answer
(A)
0.0226 m²
32
Two cones are similar. The ratio of their radii is 2:5. If the volume of the smaller cone is 16π cm³, what is the volume of the larger cone?
Answer
(D)
250π cm³
33
A rectangular garden is 4 meters wide and 6 meters long. A similar garden has a width of 8 meters. What is the length of the larger garden?
Answer
(B)
10 m
34
What is the relationship between the length scale factor and the area scale factor for mathematically similar shapes?
Answer
(C)
Area scale factor = (length scale factor) ^2
35
A map has a scale of 1:10000. The distance between two points on the map is 5 cm. What is the actual distance between the two points in km?
Answer
(A)
0.5 km
36
The height of a cone is 10 cm. A similar cone has a height of 20 cm. If the volume of the smaller cone is 50 cm³, what is the volume of the larger cone?
Answer
(D)
800 cm³
37
Two similar prisms have volumes of 27 cm³ and 125 cm³. What is the ratio of their corresponding surface areas?
Answer
(B)
9:25
38
What is the volume scale factor if the area scale factor is 25?
Answer
(C)
125
39
Two similar figures have perimeters in the ratio 3:5. If the smaller figure has an area of 18 cm², what is the area of the larger figure?
Answer
(B)
50 cm²
40
A model of a car has a volume of 250 cm³. The actual car has a volume 20 times as large. What is the volume of the real car?
Answer
(D)
50000 cm³
41
A model of a building is made to a scale of 1:50. The dimensions of a room in the model are 7.4 cm by 9.8 cm. Find the floor area of the room in the model.
Answer
(A)
72.52 cm²
42
For two shapes to be similar, which of the following conditions must be met?
Answer
A
B
43
The ratio of the surface areas of two similar solids is 9:16. What is the ratio of their volumes?
Answer
(C)
27:64
44
An artist makes a model for a large sculpture. It is 24 cm high and the finished sculpture will be 3.6m high. Find the length scale factor.
Answer
(D)
15
45
What happens to the area of a square if you increase the length of its sides by 100%?
Answer
(C)
The area quadruples.
46
What is the volume scale factor if the length scale factor is 3?
Answer
(D)
27
47
A glass is 12 cm high. How tall is a similar glass that holds twice as much?
Answer
(B)
12∛2 cm
48
The lengths of the sides of two similar rectangles are in a ratio of 3:7. If the area of the smaller rectangle is 27 cm², what is the area of the larger rectangle?
Answer
(D)
441 cm²
49
What happens to the volume of a cube if the sides are tripled in length?
Answer
(D)
The volume is multiplied by 27.
50
A statue is 10 feet tall. A miniature replica of the statue is 4 inches tall. What is the scale factor?
