Surface Area & Volume of 3-D Objects (Grade 9) — Worksheet & Memo

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Grade 9 · Surface Area & Volume

Surface Area & Volume of 3-D Objects (Grade 9)

EXAM-STYLE CLASS TEST

Marks

Duration

1 hour 5 minutes

Questions

Name:

Class:

Date:

Mark

/ 41

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 cylinder of radius 5 cm and height 10 cm (π ≈ 3,14) is …
(1)
A)157 cm³
B)785 cm³
C)314 cm³
D)1 570 cm³
1.2
The volume of ANY prism equals …
(1)
A)length × breadth × height
B)area of the CROSS-SECTION × length
C)perimeter × height
D)½ × base × height
1.3
A cube has a volume of 125 cm³. Its SURFACE AREA is …
(1)
A)25 cm²
B)150 cm²
C)750 cm²
D)125 cm²
1.4
1 000 cm³ is the same as …
(1)
A)1 mℓ
B)1 ℓ
C)10 ℓ
D)100 mℓ
1.5
If the HEIGHT of a cylinder is doubled and the radius is unchanged, the volume is multiplied by …
(1)
A)4
B)2
C)8
D)1
1.6
If the RADIUS of a cylinder is doubled and the height is unchanged, the volume is multiplied by …
(1)
A)2
B)4
C)8
D)6
1.7
The surface area of a closed cylinder is …
(1)
A)2πrh
B)2πr² + 2πrh
C)πr²h
D)πr² + 2πrh
1.8
A triangular prism has a cross-section of area 24 cm² and a length of 15 cm. Its volume is …
(1)
A)39 cm³
B)360 cm³
C)180 cm³
D)720 cm³
1.9
If ALL the dimensions of a solid are doubled, its VOLUME is multiplied by …
(1)
A)2
B)8
C)4
D)6
1.10
A rectangular tank is 40 cm by 30 cm by 25 cm. Its capacity in litres is …
(1)
A)3 ℓ
B)30 ℓ
C)300 ℓ
D)0,3 ℓ

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.

2.1
Calculate the volume of the prism.
(3)
2.2
Calculate the surface area of the prism.
(4)
2.3
A cube has sides of 5 cm. Calculate its volume, and hence its total surface area.
(3)

Question 3

[13 MARKS]

The diagram below shows a cylinder. Use π ≈ 3,14 and round off to TWO decimal places where necessary.

3.1
Write down the formula for the volume of a cylinder, and explain how it follows from "area of the cross-section × length".
(3)
3.2
Calculate the volume of the cylinder.
(3)
3.3
Calculate the total surface area of the cylinder.
(4)
3.4
The radius of the cylinder is doubled while the height stays the same. Determine by what factor the volume increases, and give a reason.
(3)

Question 4

[8 MARKS]

The diagram below shows a triangular prism.

4.1
Calculate the volume of the prism.
(3)
4.2
The prism is filled with water. Write down its capacity in millilitres, and then in litres.
(3)
4.3
Explain why the volume of ANY prism can be found by multiplying the area of its cross-section by its length.
(2)

TOTAL: 41 marks

This question paper consists of 4 questions.