Surface area Quiz (Grade 4)

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Topic:

Score: 0 / 10

Surface area — Notes & Worked Examples Show / Hide

Explanation:

The total surface area of a 3D solid is the sum of the areas of all its outer faces, measured in square units (cm² or m²). A cuboid has 6 rectangular faces in 3 identical opposite pairs: Surface Area = 2(lw + lh + wh).

For a triangular prism, add the areas of the 2 triangular ends (12 × base × height each) and the 3 rectangular sides. Be careful not to confuse the slant edge of the triangle with its perpendicular height!

Example 1: Find the total surface area of a cuboid measuring 8 cm by 5 cm by 3 cm.

2(8×5) = 80

2(8×3) = 48

2(5×3) = 30

Total = 158 cm²

Example 2: A right-angled triangular prism has ends 3 cm, 4 cm, 5 cm and length 10 cm. Find its total surface area.

2 ends = 2(12×3×4) = 12

3 sides = 30+40+50 = 120

Total = 132 cm²

One Page Guide (PDF) Surface area Worksheets

Question 1

[2 marks]

Calculate the total surface area of the cuboid

m²

Worked Solution & Answer

Find the area of all 6 rectangular faces and add them together: 2(lw + lh + wh).
220 m²

Answer: 220 m² m²

Question 2

[2 marks]

Calculate the curved surface area of the cylinder
Give your answer to 1 decimal place

mm²

Worked Solution & Answer

Surface area of a cylinder = 2π r² + 2π rh
282.7 mm²

Answer: 282.7 mm² mm²

Question 3 AQA Jun 2023 3F Q19 / 3H Q6

[2 marks]

Here is cuboid A.
Cuboid B is made from **two** of cuboid A.

volume of A : volume of B = 1 : 2
Matthew says,
“surface area of A : surface area of B must be 1 : 2 because B is made of 2 of A.”
Is Matthew correct?
Tick **one** box.
[ ] Yes [ ] No [ ] Cannot tell
Give a reason for your answer.

Worked Solution & Answer

(The volume of a cuboid is length × width × height)
When two cuboids are joined together, two touching faces are hidden inside, so the surface area of B is less than twice the surface area of A. M1 C1

Answer: No — two faces are joined inside B so they are not part of the outer surface area (e.g. 6 faces vs 10 faces)

Question Paper (PDF) • Mark Scheme (PDF)

Question 4 Eduqas Nov 2020 2F Q13

[2 marks]

(a) This solid prism is made from identical cubes. Each cube has sides of length 1 cm.
(b) The total surface area of a different cube is 144 cm².
To work out the side length of this cube, Mai does the following calculations:
√(144) = 12
12 ÷ 6 = 2
Mai’s method is incorrect.
Explain the mistake that Mai has made.

(a) This solid prism is made from identical cubes. Each cube has sides of length 1 cm. [1 mark]

Give the dimensions of a cuboid that could be made with the same number of cubes.

(b) The total surface area of a different cube is 144 cm².
To work out the side length of this cube, Mai does the following calculations:
√(144) = 12
12 ÷ 6 = 2
Mai’s method is incorrect.
Explain the mistake that Mai has made. [1 mark]

Worked Solution & Answer

(a)

Total number of unit cubes = 20
Possible cuboids: 1×1×20, 1×2×10, 2×2×5, 1×4×5. B1

Answer (a): 2 cm by 2 cm by 5 cm (or any dimensions with product 20)

(b)

She should have divided by 6 first to find the area of one face (144 / 6 = 24), and then taken the square root (√24), rather than square rooting first

Answer (b): She should have divided by 6 first to find the area of one face (144 / 6 = 24), and then taken the square root (√24), rather than square rooting first

Question Paper (PDF) • Mark Scheme (PDF)

Question 5 IGCSE Nov 2024 2F Q22 / 2H Q6

[3 marks]

The diagram shows a solid triangular prism.

Work out the total surface area of the triangular prism.

cm²

Worked Solution & Answer

Two triangular ends = 2 × (½ × 8 × 6) = 48 cm² M1
Three rectangular faces = (15 × 8) + (15 × 6) + (15 × 10) = 120 + 90 + 150 = 360 cm² M1
Total = 48 + 360 = 408 cm² A1

Answer: 408 cm²

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 AQA Nov 2019 2F Q22

[3 marks]

Here is a cuboid.
The two largest faces are blue.
The other four faces are green.

Work out both areas and state Yes or No.

Is the total blue area greater than the total green area?
You must show your working.

Answer

Worked Solution & Answer

The dimensions are 9 cm, 5 cm, and 3 cm M1
The two largest faces have dimensions 9 cm by 5 cm
Total blue area = 2 × (9 × 5) = 2 × 45 = 90 cm²
The other four faces: M1
Two of 9 cm by 3 cm: 2 × 27 = 54 cm²
Two of 5 cm by 3 cm: 2 × 15 = 30 cm²
Total green area = 54 + 30 = 84 cm²
Since 90 cm² > 84 cm², the total blue area is greater than the total green area. A1

Answer: Answer Yes

Question Paper (PDF) • Mark Scheme (PDF)

Question 7

[3 marks]

A cube is placed on top of a cuboid, as shown in the diagram, to form a solid.

The cube has edges of length 4 cm.
The cuboid has dimensions 7 cm by 6 cm by 5 cm.
Work out the total surface area of the solid.

cm²

Worked Solution & Answer

Cuboid surface area = 2(7×6 + 7×5 + 6×5) = 2(42 + 35 + 30) = 214 cm² M1
4 vertical faces of cube = 4 × (4 × 4) = 64 cm² M1
Total = 214 + 64 = 278 cm² A1

Answer: 278 cm²

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 AQA Nov 2022 2H Q8

[3 marks]

(a) The total length of all edges of the cuboid is 80 cm and volume > 200 cm³. Work out one possible set of whole number values for w, x and y. [2 marks]
8 (b) Circle the expression for the total surface area of a cube of side 3a cm. [1 mark]

(a) Here is a cuboid.
w, x and y are **different** whole numbers. [2 marks]

The total length of **all** the edges of the cuboid is 80 cm
The volume is **greater** than 200 cm³
Work out one possible set of values for w, x and y.

(b) Here is a solid cube. [1 mark]

Circle the expression for the **total** surface area in cm²
36a 54a 36a² 54a²

Worked Solution & Answer

(a)

(The volume of a cuboid is length × width × height)
4(w + x + y) = 80 ⇒ w + x + y = 20 M1
Try 8, 7, 5: 8 + 7 + 5 = 20 and 8 × 7 × 5 = 280 > 200 A1

Answer (a): w = 8, x = 7, y = 5

(b)

(The area of a circle is πr²)
Area of one face = (3a)² = 9a²
Total surface area = 6 × 9a² = 54a² B1

Answer (b): 54a²

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 AQA Jun 2018 1H Q18

[5 marks]

Here is a tunnel for a toy train.
The diagram shows the cross section of the tunnel.

AD is a semicircular arc of radius 10 cm
BC is a semicircular arc of radius 7 cm
The length of the tunnel is 30 cm
Work out the total area of all six faces of the tunnel.
Give your answer in terms of π.

Answer cm²

Worked Solution & Answer

The 6 faces are: M1
1 & 2. Two cross-section faces: each is 12π(10² - 7²) = 12π(100 - 49) = 25.5π M1
Two faces = 51π.
3. Outer curved face: π × 10 × 30 = 300π. M1
4. Inner curved face: π × 7 × 30 = 210π.
5 & 6. Two rectangular base faces: each has width 10 - 7 = 3 cm and length 30 cm, area = 3 × 30 = 90 cm² M1
Two bases = 180 cm²
Total surface area = 51π + 300π + 210π + 180 = 561π + 180 cm². A1

Answer: Answer 561π + 180 cm²

Question Paper (PDF) • Mark Scheme (PDF)

Question 10

[5 marks]

Here is a cuboid of length 10 cm and width 4 cm.

(a) Work out the height of the cuboid. [2 marks]

(b) Work out the total surface area of this cuboid. [3 marks]

cm²

Worked Solution & Answer

(a)

(The volume of a cuboid is length × width × height)
200 ÷ (10 × 4) = 5 cm M1 A1

Answer (a): 5 cm

(b)

2 × (6×5 + 6×3 + 5×3) = 2 × (30 + 18 + 15) = 126 cm² M2 A1

Answer (b): 126 cm²

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 30 marks)

Surface area Worksheets Next: Volume of a cuboid →

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