Surface Area and Volume: Complete Guide — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 8 · Measurement

Surface Area and Volume: Complete Guide

MARKING GUIDELINE

Marks

Duration

1 hour

Questions

Name:

Class:

Date:

Mark

/ 40

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
The volume of a rectangular prism 6 cm by 4 cm by 5 cm is …
(1)
A)15 cm³
B)120 cm³✓
C)148 cm³
D)30 cm³
Answer: B — V = l × b × h.
- A — added the three dimensions
- C — that is the SURFACE AREA
- D — used only two dimensions
1.2
The surface area of that same prism is …
(1)
A)120 cm²
B)148 cm²✓
C)74 cm²
D)15 cm²
Answer: B — 2(6×4 + 6×5 + 4×5) = 2(24 + 30 + 20).
- A — that is the VOLUME
- C — forgot to double
- D — added the dimensions
1.3
A cube has sides of 4 cm. Its volume is …
(1)
A)16 cm³
B)64 cm³✓
C)96 cm³
D)12 cm³
Answer: B — 4³ = 64.
- A — that is 4 SQUARED
- C — that is the surface area
- D — multiplied 4 by 3
1.4
The surface area of that cube is …
(1)
A)64 cm²
B)96 cm²✓
C)16 cm²
D)24 cm²
Answer: B — 6 faces of 4²: 6 × 16.
- A — that is the VOLUME
- C — that is ONE face
- D — used 6 × 4
1.5
The volume of ANY prism is …
(1)
A)length × breadth × height, always
B)area of the cross-section × length✓
C)perimeter × length
D)half the base × height
Answer: B — A prism is its cross-section stacked along its length.
- A — that works only for a rectangular prism
- C — perimeter gives a surface, not a volume
- D — that is the area of a triangle
1.6
A triangular prism has a cross-section of area 20 cm² and a length of 12 cm. Its volume is …
(1)
A)32 cm³
B)240 cm³✓
C)120 cm³
D)480 cm³
Answer: B — 20 × 12 = 240.
- A — added instead of multiplying
- C — halved the answer unnecessarily
- D — doubled the answer
1.7
Volume is measured in cm³ but surface area in cm² because …
(1)
A)volume is bigger
B)volume fills THREE dimensions and area covers two✓
C)area is always smaller
D)the units are interchangeable
Answer: B — Three lengths multiplied give a cubic unit; two give a square unit.
- A — the numbers are not what decide the unit
- C — a thin sheet can have a large area and little volume
- D — they are not interchangeable
1.8
1 cm³ is the same as …
(1)
A)1 ℓ
B)1 mℓ✓
C)10 mℓ
D)1 000 ℓ
Answer: B — 1 cm³ = 1 mℓ, and 1 000 cm³ = 1 ℓ.
- A — that is 1 000 cm³
- C — 1 cm³ is 1 mℓ, not 10
- D — far too large — that is a cubic metre
1.9
A box holds 2 000 cm³. In litres that is …
(1)
A)20 ℓ
B)2 ℓ✓
C)200 ℓ
D)0,2 ℓ
Answer: B — 2 000 ÷ 1 000 = 2 ℓ.
- A — divided by 100
- C — divided by 10
- D — divided by 10 000
1.10
If ALL the dimensions of a box are doubled, its volume is multiplied by …
(1)
A)2
B)8✓
C)4
D)6
Answer: B — Volume scales by the CUBE of the length factor: 2³.
- A — that is the LENGTH factor
- C — that is the AREA factor
- D — that is the number of faces

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[10 MARKS]

The diagram below shows a rectangular prism (a box).

2.1
Write down the formula for the volume of a rectangular prism, and explain why its SURFACE AREA needs a different formula.
(3)
V = l × b × h (1)
Volume multiplies THREE dimensions, because it measures the space the prism fills (1)
Surface area ADDS the areas of the six flat faces, which gives 2(lb + lh + bh) (1)
2.2
Calculate the volume of the box.
(3)
V = 6 × 3 × 2 (2)
= 36 cm³ (1)
2.3
A different box measures 5 cm by 4 cm by 2 cm. Calculate its surface area.
(4)
SA = 2(lb + lh + bh) (1)
= 2(20 + 10 + 8) (2)
= 76 cm² (1)

Question 3

[11 MARKS]

The diagram below shows a cube with sides of 4 cm.

3.1
Calculate the volume of the cube, and hence its total surface area.
(3)
V = 4³ = 64 cm³ (2)
A cube has 6 identical square faces, so SA = 6 × 4² = 96 cm² (1)
3.2
Calculate the surface area of the cube.
(3)
A cube has 6 identical square faces (1)
SA = 6 × 4² (1) = 96 cm² (1)
3.3
The cube is filled with water. Determine the capacity of the cube in millilitres.
(3)
1 cm³ = 1 mℓ (1)
64 cm³ = 64 mℓ (2)
3.4
Explain why volume is measured in cm³ but surface area in cm².
(2)
Volume fills three dimensions — length, breadth and height (1); surface area covers only the two-dimensional faces (1)

Question 4

[9 MARKS]

The diagram below shows a triangular prism.

4.1
Calculate the area of the triangular cross-section, and state which of the two measurements you used is the perpendicular height.
(3)
A = 12 × 8 × 5 = 20 cm² (2)
The 5 cm is the perpendicular height — it is measured at right angles to the 8 cm base (1)
4.2
Hence calculate the volume of the prism.
(3)
V = area of cross-section × length (1)
= 20 × 10 (1) = 200 cm³ (1)
4.3
A different prism has a cross-sectional area of 15 cm² and a volume of 120 cm³. Calculate its length, and state what happens to the volume if that length is doubled.
(3)
V = area of cross-section × length, so length = 120 ÷ 15 (1)
= 8 cm (1)
The volume DOUBLES to 240 cm³, because volume is directly proportional to length (1)

TOTAL: 40 marks

This question paper consists of 4 questions.