Mathematics for IGCSE & O level - Mensuration (Section 13)
1
A circle has a radius of 2 cm. What is its area, rounded to two decimal places? (Use π ≈ 3.14)
Answer
(B)
12.56 cm²
2
Which formula should be used to find the area of a minor segment?
Answer
(A)
Area of a sector - Area of a triangle
3
How is the volume of a prism calculated?
Answer
(A)
Area of cross-section x length
4
What is the angle at the center of the circle when using the arc length?
Answer
(A)
Θ
5
A cylinder and a cone each have base radius 5.6cm. A cylinder is 6.2m high. Find its volume.
Answer
(B)
610.7 cm³
6
A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (use pi = 3.14)
Answer
(B)
282.6 cm³
7
If the area of a rectangle is 35cm² and its width is 5cm, what is its length?
Answer
(A)
7cm
8
How do you calculate the area of a composite shape made up of rectangles and triangles?
Answer
(C)
Calculate the area of each individual shape and sum them.
9
What is the formula for the volume of a cone?
Answer
(D)
1/3πr²h
10
Which shapes can be split to find the total area?
Answer
A
B
C
11
Calculate the volume of a prism. 10cm long with each of these cross sections: Rectangle 5cm x 3cm
Answer
(A)
150 cm³
12
Calculate the total surface area of a solid hemisphere of radius 5cm.
Answer
(A)
235.6 cm²
13
What does 'r' represent in the formula for the area of a circle (A = πr²)?
Answer
(C)
Radius
14
What is the area of a square whose side is 4m?
Answer
(B)
16 m²
15
Calculate the surface area of a solid hemisphere with base radius 7.1cm and slant height 9.7cm.
Answer
(B)
363.5 cm²
16
Which of the following statements is/are true about the volume of a pyramid?
Answer
A
B
D
17
What is the formula for the area of a rectangle?
Answer
(C)
length x width
18
If the radius of a circle is r, what is the formula for its circumference?
Answer
(B)
2πr
19
A cone has a base radius of 5cm and a slant height of 13cm. Calculate the total surface area of the cone.
Answer
A
B
C
20
Which equation can be used to find the volume of a rectangular prism?
Answer
(A)
V = l x w x h
21
What is the relationship between the volume of a cone and a cylinder with the same base radius and height?
Answer
(C)
The volume of the cone is one-third the volume of the cylinder.
22
A circle has a circumference of 31.4 cm. What is its approximate diameter? (Use π ≈ 3.14)
Answer
(B)
10 cm
23
Which formula(s) can be used to find the surface area of a sphere?
Answer
(B)
4πr²
24
To find the area of a complex shape, it can be split into two __.
Answer
(C)
Rectangles and/or triangles
25
Which of the following involves a formula using the base and height?
Answer
B
C
D
26
What must be known to calculate the volume of a rectangular prism?
Answer
A
B
C
27
What does π (pi) represent in geometric calculations?
Answer
(B)
The ratio of a circle's circumference to its diameter
28
If a square has a side length of 5 cm, what is its perimeter?
Answer
(B)
20 cm
29
Which of these is a composite shape?
Answer
(D)
A shape made from combining a rectangle and a triangle
30
A room is 5m long and 4m wide. How much floor space does it cover?
Answer
(C)
20 m²
31
Which of the following shapes is a prism?
Answer
(B)
A cube
32
If a shape is made up of a rectangle and a triangle, how would you find its total area?
Answer
(C)
Add the area of the rectangle and the area of the triangle.
33
What is the formula for the area of a parallelogram?
Answer
(B)
A= base * height
34
A tower of a castle has walls in the form of a cylinder and a roof in the shape of a cone. The diameter of the tower is 5.6 m and the height of the wall is 12 m. The roof has a height of 6.2 m. What is the volume of the tower?
Answer
(A)
234.7 m³
35
What is the formula to work out the perimeter of a sector?
Answer
(A)
Arc length + 2r
36
If a sphere has a radius of 7cm, what is the formula for its surface area?
Answer
(B)
4 * π * 7²
37
A solid hemisphere has a radius of 2 cm. What is its volume?
Answer
(D)
25.13 cm³
38
If the cross section is a rectangle, what is the formula to find the area?
Answer
(A)
Length x width
39
What is the formula for the volume of a prism?
Answer
(A)
Area of cross-section * length
40
What is the formula for the area of a rectangle?
Answer
(A)
Length x Width
41
If a hemisphere is half of a sphere, what is the formula for calculating its volume?
Answer
(B)
2/3πr³
42
What is the formula for the circumference of a circle, given its diameter (d)?
Answer
(C)
C = πd
43
If a circle has a diameter of 10cm, what is its area? (Use pi = 3.14)
Answer
(B)
78.5 cm²
44
A rectangular garden is 12 meters long and has an area of 60 square meters. What is the width of the garden?
Answer
(A)
5 m
45
A cone has slant height 7cm and curved surface area 68 cm². Calculate the total surface area of the cone.
Answer
(A)
96.8 cm²
46
Which shapes are considered to be pyramids?
Answer
A
B
D
47
A box has a volume of 120 cm³. If its length is 6cm and its width is 5cm, what is its height?
Answer
(B)
4cm
48
How is the height of a cylinder measured?
Answer
(B)
The distance between the centers of the two circular bases.
49
A rectangle has a perimeter of 28cm and one side is 8cm. How long is the other side?
Answer
(B)
6cm
50
Which units of measure are used for length, area, volume, and capacity?
