Surface Area and Volume: Complete Guide — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 8 · Measurement

Surface Area and Volume: Complete Guide

EXAM-STYLE CLASS TEST

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
1.2
The surface area of that same prism is …
(1)
A)120 cm²
B)148 cm²
C)74 cm²
D)15 cm²
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
1.4
The surface area of that cube is …
(1)
A)64 cm²
B)96 cm²
C)16 cm²
D)24 cm²
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
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
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
1.8
1 cm³ is the same as …
(1)
A)1 ℓ
B)1 mℓ
C)10 mℓ
D)1 000 ℓ
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
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 grid — circle your answers for Question 1

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)
2.2
Calculate the volume of the box.
(3)
2.3
A different box measures 5 cm by 4 cm by 2 cm. Calculate its surface area.
(4)

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)
3.2
Calculate the surface area of the cube.
(3)
3.3
The cube is filled with water. Determine the capacity of the cube in millilitres.
(3)
3.4
Explain why volume is measured in cm³ but surface area in cm².
(2)

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)
4.2
Hence calculate the volume of the prism.
(3)
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)

TOTAL: 40 marks

This question paper consists of 4 questions.