Mathematics for IGCSE & O level - Mensuration (Section 11)
1
If a solid hemisphere has a radius of 4 cm, what is its volume?
Answer
(D)
100 cm³
2
In what units should area always be expressed?
Answer
(C)
Square Units
3
When working out to solve a problem, what is the first step to follow?
Answer
(B)
Read the question carefully
4
A rectangular field is 20m long and has an area of 100m². What is the width of the field?
Answer
(A)
5 m
5
A pyramid has a square base with a side of 4cm and a perpendicular height of 9cm. What is the volume of the pyramid?
Answer
(A)
48 cm³
6
What information is needed to calculate the area of a rectangle?
Answer
A
B
7
What do you need to find the area of a triangle?
Answer
A
B
8
What is the approximate circumference of a circle with a radius of 14cm?
Answer
(C)
176 cm
9
How is the slant height of a cone related to its radius and height?
Answer
(B)
Slant height = √(radius² + height²)
10
Calculate the volume of a prism. 10cm long with each of these cross sections: Triangle with base 2cm, height 8.5cm
Answer
(A)
85 cm³
11
What is the volume of a prism?
Answer
(A)
area of cross-section x length
12
Which of the following shapes would need the Pythagorean Theorem to calculate its area?
Answer
(C)
A right-angled triangle
13
Which of the following are key parts of the formula for the area of a sector of a circle?
Answer
A
B
14
Which formula is used to calculate the area of a triangle?
Answer
(C)
Area = 1/2 * base * height
15
A vase is a prism with a cross section as shown. The internal measurements are as shown. How much water can the vase hold? Give your answer in litres. (Remember that 1 litre = 1000cm³). The vase is a right angle traingle with sides 12cm x 15cm and 10cm high.
Answer
(A)
0.90 Litres
16
What is an important part of every answer to a mensuration problem?
Answer
(B)
The correct units are included.
17
What is the formula for arc length?
Answer
(B)
(θ/360) x 2πr
18
Which of the following formulas is used to calculate the curved surface area of a cylinder?
Answer
(A)
2πrh
19
What is the relationship between the radius (r) and the diameter (d) of a circle?
Answer
A
B
20
What is the formula for the surface area of a solid hemisphere (including the base)?
Answer
(B)
3πr²
21
Which of the following are required to calculate the volume of a prism?
Answer
A
B
22
What must you remember when giving an answer for area?
Answer
(A)
That all units are square units.
23
What do you need to know to calculate the volume of a cylinder?
Answer
A
B
24
A sphere has a surface area of 1274 cm². Calculate its radius.
Answer
(A)
10.1 cm
25
What is the relationship between the surface area of a sphere and the area of its great circle?
Answer
(C)
The surface area is four times the area of the great circle.
26
A pyramid has a volume of 50 cm³ and a base area of 15 cm². What is the height of the pyramid?
Answer
(D)
10 cm
27
A parallelogram has a base of 7cm and a height of 4 cm. What is the area?
Answer
(A)
28 cm²
28
What formula is used to determine the volume of a pyramid?
Answer
(A)
1/3 x area of base x height
29
A cone has a base with an area of 28.26 cm² and a height of 6 cm. What is the volume of the cone?
Answer
(A)
56.52 cm³
30
The surface area of a sphere is 64π cm². What is the radius of the sphere?
Answer
(A)
4 cm
31
What is the area of a triangle with a base of 10 cm and a height of 5 cm?
Answer
(B)
25 cm²
32
What is the area of a parallelogram with a base of 6 cm and a height of 8 cm?
Answer
(B)
48 cm²
33
A sphere containing liquid has a capacity of 7.15 litres. Calculate its radius.
Answer
(B)
11.8 cm
34
What is the volume of a hemisphere with a radius of 6 cm?
Answer
(C)
226.2 cm³
35
What is the total surface area of a cylinder with a radius of 3cm and a height of 7cm?
Answer
(A)
188.5 cm²
36
A chocolate box is in the shape of a triangular prism. Calculate its volume. The triangle is 6.2cm height, 5cm base and prism is 12cm long.
Answer
(A)
186 cm³
37
What units are used to measure volume?
Answer
(B)
Cubic units
38
The circumference of a circle can be calculated using the formula: C = πd. What does 'd' represent?
Answer
(B)
Diameter
39
Which of the following shape has a base and curved surface?
Answer
(C)
Cone
40
What is the relationship between a circle and a sector?
Answer
(A)
A sector is a part of a circle.
41
Which is the best method to calculate the volume of an irregular shape?
Answer
(C)
Use water displacement.
42
If the height of a cylinder is doubled, how is its volume affected?
Answer
(A)
The volume doubles.
43
What is the area of a parallelogram with a base of 12cm and a height of 5cm?
Answer
(A)
60 cm²
44
The volume of a cuboid is calculated by:
Answer
(C)
length * width * height
45
What are the Key Points used for?
Answer
(B)
To study the formulas and properties
46
The volume of a prism is always calculated using:
Answer
(C)
The area of its cross-section x length
47
A trapezium has parallel sides of 5cm and 7cm and a height of 3cm. What is the area?
Answer
(C)
21 cm²
48
What is the formula for the area of a parallelogram?
Answer
(C)
base x height
49
What is a 'frustum' in the context of 3D shapes?
Answer
(B)
The portion of a cone or pyramid remaining after the top is cut off
