Sec 1 Maths Volume and surface area worksheet with answers

A free Sec 1 Maths worksheet on volume and surface area: 8 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 Maths worksheet: Volume and surface area

Total: 30 marksSuggested time: 45 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

The total surface area of the closed cuboid is

288

cm². Find the value of

h

Answercm[2]

The diagram shows a cylindrical pencil holder, open at the top. Find its total surface area, correct to 3 significant figures.

Answercm²[2]

The diagram shows a triangular prism. The dashed line is perpendicular to the base of the triangle. Find its volume.

Answercm³[2]

The diagram shows a fish pond in the shape of a prism of length

200

cm. It is empty, and water flows in at a constant rate of

12

litres per minute. It is full after

8

minutes. Find the area of its cross-section, in cm².

Answercm²[3]

Section B

(a)The diagram shows a prism with a trapezium cross-section. The dashed line is perpendicular to the parallel sides. Find its volume.

Answer (a)cm³[2]

(b)A container holds

0.65

m³. Express this volume in cm³.

Answer (b)cm³[2]

(a)A rectangular fish tank measures

100

cm by

60

cm by

50

cm. Find its capacity, in litres.

Answer (a)litres[2]

(b)The diagram shows a toy box in the shape of a cuboid, open at the top. Its outside is painted with paint that costs $15 per m². Find the cost of the paint needed.

Answer (b)$[2]

(a)A rectangular piece of card,

27

cm by

20

cm, is rolled up so that its two edges of length

20

cm just meet, without overlapping. It forms the curved surface of a cylinder of height

20

cm. Find the radius of the cylinder, correct to 3 significant figures.

Answer (a)cm[2]

(b)The diagram shows a prism with an L-shaped cross-section. All the corners of the cross-section are right angles. Find the total surface area of the prism.

Answer (b)cm²[3]

(a)The diagram shows a wooden shelf bracket. All the corners of its cross-section are right angles. Find its volume.

Answer (a)cm³[2]

(b)

4

identical tins of paint, each of radius

2

cm and height

12

cm, stand upright in a closed rectangular box:

2

along its length and

2

across its width. They fit exactly, touching each other, the sides, the top and the bottom of the box. Find the volume of air space in the box, correct to 3 significant figures.

Answer (b)cm³[3]

(c)The diagram shows a ramp in the shape of a triangular prism. Its cross-section is a right-angled triangle. Find its total surface area.

Answer (c)cm²[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

h = 9

cm[2]

2(6 \times 6 + 6h + 6h) = 288

72 + 24h = 288

24h = 216

h = \dfrac{216}{24}

h = 9

Question 2

Answer:

= 179

cm² (3 s.f.)[2]

\text{TSA} = 2\pi rh + \pi r^2

= 2\pi(3)(8) + \pi(3)^2

= 179.0707\ldots

= 179

cm² (3 s.f.)

Question 3

Answer:

= 168

cm³[2]

\text{Area} = \dfrac{1}{2} \times 7 \times 4

= 14

cm²

V = 14 \times 12

= 168

cm³

Question 4

Answer:

\phantom{A} = 480

cm²[3]

\text{Volume} = 12 \times 8

\phantom{\text{Volume}} = 96

litres

96 \text{ litres} = 96 \times 1000

\phantom{96 \text{ litres}} = 96000

cm³

A = \dfrac{96000}{200}

\phantom{A} = 480

cm²

Question 5

(a)Answer:

= 384

cm³[2]

\text{Area} = \dfrac{1}{2} \times (3 + 13) \times 4

= 32

cm²

V = 32 \times 12

= 384

cm³

(b)Answer:

= 650\,000

cm³[2]

1 \text{ m}^3 = 100 \times 100 \times 100 \text{ cm}^3

= 1\,000\,000 \text{ cm}^3

0.65 \text{ m}^3 = 0.65 \times 1\,000\,000 \text{ cm}^3

= 650\,000

cm³

Question 6

(a)Answer:

= 300

litres[2]

V = 100 \times 60 \times 50

= 300\,000

cm³

\text{Capacity} = \dfrac{300000}{1000}

= 300

litres

(b)Answer: The paint costs $21.60.[2]

\text{Area} = (80 \times 50) + 2(80 \times 40) + 2(50 \times 40)

= 14\,400

cm²

\dfrac{14400}{10\,000} = 1.44

m²

1.44 \times 15 = 21.60

The paint costs $21.60.

Question 7

(a)Answer:

= 4.30

cm (3 s.f.)[2]

2\pi r = 27

r = \dfrac{27}{2\pi}

= 4.2971\ldots

= 4.30

cm (3 s.f.)

(b)Answer:

= 378

cm²[3]

\text{Cross-section} = 6 \times 5 - 3 \times 2

= 24

cm²

\text{Perimeter} = 6 + 3 + 3 + 2 + 3 + 5

= 22

\text{TSA} = 2 \times 24 + 22 \times 15

= 378

cm²

Question 8

(a)Answer:

= 420

cm³[2]

\text{Area} = 10 \times 6 - 6 \times 3

= 42

cm²

V = 42 \times 10

= 420

cm³

(b)Answer:

= 165

cm³ (3 s.f.)[3]

Length

= 2 \times 4

= 8

cm, width

= 2 \times 4

= 8

\text{Box} = 8 \times 8 \times 12

\phantom{\text{Box}} = 768

cm³

\text{Cans} = 4 \times \pi(2)^2(12)

= 603.1857\ldots

cm³

\text{Air} = 768 - 4 \times \pi(2)^2(12)

= 164.8142\ldots

= 165

cm³ (3 s.f.)

(c)Answer:

= 132

cm²[3]

\text{Triangle} = \dfrac{1}{2} \times 4 \times 3

= 6

cm²

\text{Perimeter} = 4 + 3 + 5

= 12

\text{TSA} = 2 \times 6 + 12 \times 10

= 132

cm²

Practice questions by skill

Sec 1 Maths Volume and surface area worksheet with answers

In the print window, choose Save as PDF to download it.

Need the formulas first? Read the Volume and surface area notes. Or practise it online with step-by-step help when you get one wrong.

Answers and worked solutions

Question 1

Answer:

h = 9

cm[2]

2(6 \times 6 + 6h + 6h) = 288

72 + 24h = 288

24h = 216

h = \dfrac{216}{24}

h = 9

Question 2

Answer:

= 179

cm² (3 s.f.)[2]

\text{TSA} = 2\pi rh + \pi r^2

= 2\pi(3)(8) + \pi(3)^2

= 179.0707\ldots

= 179

cm² (3 s.f.)

Question 3

Answer:

= 168

cm³[2]

\text{Area} = \dfrac{1}{2} \times 7 \times 4

= 14

cm²

V = 14 \times 12

= 168

cm³

Question 4

Answer:

\phantom{A} = 480

cm²[3]

\text{Volume} = 12 \times 8

\phantom{\text{Volume}} = 96

litres

96 \text{ litres} = 96 \times 1000

\phantom{96 \text{ litres}} = 96000

cm³

A = \dfrac{96000}{200}

\phantom{A} = 480

cm²

Question 5

(a)Answer:

= 384

cm³[2]

\text{Area} = \dfrac{1}{2} \times (3 + 13) \times 4

= 32

cm²

V = 32 \times 12

= 384

cm³

(b)Answer:

= 650\,000

cm³[2]

1 \text{ m}^3 = 100 \times 100 \times 100 \text{ cm}^3

= 1\,000\,000 \text{ cm}^3

0.65 \text{ m}^3 = 0.65 \times 1\,000\,000 \text{ cm}^3

= 650\,000

cm³

Question 6

(a)Answer:

= 300

litres[2]

V = 100 \times 60 \times 50

= 300\,000

cm³

\text{Capacity} = \dfrac{300000}{1000}

= 300

litres

(b)Answer: The paint costs $21.60.[2]

\text{Area} = (80 \times 50) + 2(80 \times 40) + 2(50 \times 40)

= 14\,400

cm²

\dfrac{14400}{10\,000} = 1.44

m²

1.44 \times 15 = 21.60

The paint costs $21.60.

Question 7

(a)Answer:

= 4.30

cm (3 s.f.)[2]

2\pi r = 27

r = \dfrac{27}{2\pi}

= 4.2971\ldots

= 4.30

cm (3 s.f.)

(b)Answer:

= 378

cm²[3]

\text{Cross-section} = 6 \times 5 - 3 \times 2

= 24

cm²

\text{Perimeter} = 6 + 3 + 3 + 2 + 3 + 5

= 22

\text{TSA} = 2 \times 24 + 22 \times 15

= 378

cm²

Question 8

(a)Answer:

= 420

cm³[2]

\text{Area} = 10 \times 6 - 6 \times 3

= 42

cm²

V = 42 \times 10

= 420

cm³

(b)Answer:

= 165

cm³ (3 s.f.)[3]

Length

= 2 \times 4

= 8

cm, width

= 2 \times 4

= 8

\text{Box} = 8 \times 8 \times 12

\phantom{\text{Box}} = 768

cm³

\text{Cans} = 4 \times \pi(2)^2(12)

= 603.1857\ldots

cm³

\text{Air} = 768 - 4 \times \pi(2)^2(12)

= 164.8142\ldots

= 165

cm³ (3 s.f.)

(c)Answer:

= 132

cm²[3]

\text{Triangle} = \dfrac{1}{2} \times 4 \times 3

= 6

cm²

\text{Perimeter} = 4 + 3 + 5

= 12

\text{TSA} = 2 \times 6 + 12 \times 10

= 132

cm²