Cylinders Quiz (Grade 4)

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Score: 0 / 10

Cylinders — Notes & Worked Examples Show / Hide

Explanation:

A cylinder with radius r and height h is a circular prism, so its Volume is the area of the circular base times the height: Volume = πr²h.

For the total surface area of a solid cylinder, unroll the curved side into a rectangle of width 2πr (the circumference) and height h, and add the two circular ends: Total Surface Area = 2πr² + 2πrh.

Example 1: A cylinder has radius 4 cm and height 10 cm. Calculate its volume to 1 d.p.

V = πr²h

= π × 4² × 10 = 160π

= 502.7 cm³

Example 2: Calculate the total surface area of a solid cylinder with radius 4 cm and height 10 cm to 1 d.p.

2 ends = 2π(4²) = 32π

Curved = 8π×10 = 80π

112π = 351.9 cm²

One Page Guide (PDF) Cylinders Worksheets

Question 1

[2 marks]

Calculate the volume of the cylinder
Give your answer to 1 decimal place

cm³

Worked Solution & Answer

(The volume of a cylinder is πr²h) B1

Answer: 628.3 cm³ cm³

Question 2

[2 marks]

Calculate the volume of the triangular prism

m³

Worked Solution & Answer

(The volume of a prism is area of cross-section × length) B1

Answer: 420 m³ m³

Question 3 IGCSE Jun 2025 1F Q24 / 1H Q7

[3 marks]

Here is a solid cylinder.

The radius of the cylinder is 8 cm
The height of the cylinder is h cm
The volume of the cylinder is 3892 cm³
Work out the value of h
Give your answer correct to one decimal place.

h =

Worked Solution & Answer

(The volume of a cylinder is πr²h)
π × 8² × h = 3892 M2
⇒ h = 3892 ÷ (64π) = 19.357... = 19.4 A1

Answer: h = 19.4

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Question 4 IGCSE Jun 2024 1F Q23 / 1H Q8

[3 marks]

A cylinder is placed on a table.

The volume of the cylinder is 1575 cm³
The force exerted by the cylinder on the table is 84 newtons.
Work out the pressure on the table due to the cylinder.

newtons/cm²

Worked Solution & Answer

(The volume of a cylinder is πr²h)
Base area of cylinder = Volume ÷ height = 1575 ÷ 21 = 75 cm² M2
Pressure = force ÷ area = 84 ÷ 75 = 1.12 newtons/cm² A1

Answer: 1.12 newtons/cm²

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Question 5 AQA Jun 2024 3H Q21

[3 marks]

A cylinder, C, and a sphere, S, each have radius r
C has height h

(a) @@TABULAR₀@@
volume of C = volume of S
Work out the ratio r : h
You **must** show your working. [3 marks]

Answer

Worked Solution & Answer

(a)

πr²h = 4/3 πr³ M1
⇒ h = 4/3 r M1
⇒ 3h = 4r
⇒ r : h = 3 : 4. A1

Answer (a): Answer 3 : 4

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Question 6

[4 marks]

The diagram shows a solid shape made from a cylinder and a cone.

Work out the vertical height of the cone.
You must show all your working.

The cone has a base radius of 8 cm.
The cylinder has a radius of 8 cm.
The vertical height of the cone is three times the height of the cylinder.
The volume of the solid shape is 640π cm³

Worked Solution & Answer

(The volume of a cylinder is πr²h)
Let cylinder height = H M1
Cone height h = 3H
Radius r = 8 cm M1
Volume of cylinder = π r² H = π × 8² × H = 64π H
Volume of cone = 1/3 π r² h = 1/3 π × 8² × 3H = 64π H M1
Total volume = 64π H + 64π H = 128π H = 640π ⇒ H = 640 ÷ 128 = 5 cm
Height of cone h = 3 × 5 = 15 cm. A1

Answer: 15 cm

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Question 7 AQA Nov 2021 3H Q13

[4 marks]

A box is the shape of half a cylinder on top of a cuboid.

Work out the volume of the box.

Answer cm³

Worked Solution & Answer

(The volume of a cuboid is length × width × height)
Cuboid volume = 26 × 15 × 4 = 1560 cm³ M1
Half cylinder has radius r = 26 ÷ 2 = 13 cm and length h = 15 cm M1
Half cylinder volume = 12 × π × 13² × 15 = 1267.5π ≈ 3981.97 cm³ M1
Total volume = 1560 + 3981.97 = 5541.97 cm³ (or 5540 to 5542). A1

Answer: Answer 5542 cm³

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Question 8 AQA Nov 2019 1H Q9

[4 marks]

Here are two solids.

Which solid has the greater volume?
You must show your working.

Cylinder: radius 4 cm, height 10 cm
Hemisphere: radius 6 cm
volume of a hemisphere = 23π r³ where r is the radius

Answer

Worked Solution & Answer

(The volume of a cylinder is πr²h)
Volume of cylinder = π r² h = π × 4² × 10 = 160π cm³ M2
Volume of hemisphere = 23 π r³ = 23 π × 6³ = 23 × 216 × π = 144π cm³ M1
Since 160π > 144π, the cylinder has the greater volume. A1

Answer: Answer Cylinder

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Question 9 IGCSE Jun 2018 2F Q19 / 2H Q6

[4 marks]

The diagram shows two cylinders, **A** and **B**.

Cylinder **A** has height 1.6 m and radius 0.56 m.

(a) Work out the curved surface area of cylinder **A**.
Give your answer in m² correct to 3 significant figures. [2 marks]

m²

(b) Work out the radius of cylinder **B**. [2 marks]

Worked Solution & Answer

(a)

2 × π × 0.56 × 1.6 = 5.6297… = 5.63 m² M1 A1

Answer (a): 5.63 m²

(b)

0.56 × (0.6 ÷ 1.6) = 0.56 × 0.375 = 0.21 m M1 A1

Answer (b): 0.21 m

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Question 10

[5 marks]

Jeremy has to cover 3 tanks completely with paint.
Each tank is in the shape of a cylinder with a top and a bottom.
The tank has a diameter of 1.6 m and a height of 1.8 m.

Jeremy has 7 tins of paint.
Each tin of paint covers 5 m²
Has Jeremy got enough paint to cover completely the 3 tanks?
You must show how you get your answer.

Worked Solution & Answer

Radius r = 0.8 m M2
Surface area of 1 tank = 2π(0.8)² + 2π(0.8)(1.8) = 1.28π + 2.88π = 4.16π = 13.069 m² M2
Total area for 3 tanks = 3 × 13.069 = 39.21 m². 7 tins cover 7 × 5 = 35 m² < 39.21 m², so No. A1

Answer: No, 3 tanks have total surface area 39.2 m² > 35 m² covered by 7 tins (or needs 7.84 tins → 8 tins)

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Score: 0 / 10 (0 / 34 marks)

Cylinders Worksheets Next: Plans and elevations →

Grade 4 Quizzes

24 Topics

4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction