Sec 1 G2 Maths Volume and surface area worksheet with answers

A free Sec 1 G2 Maths worksheet on volume and surface area: 7 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 G2 Maths worksheet: Volume and surface area

Total: 30 marksSuggested time: 50 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

Express

12

m³ in cm³.

Answercm³[2]

The diagram shows a cylindrical tin, closed at both ends. Find its total surface area, correct to 3 significant figures.

Answercm²[2]

The volume of the cuboid is

3000

cm³. Find the value of

h

Answercm[2]

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.

Answercm²[3]

Section B

(a)The diagram shows a cardboard box in the shape of a cuboid. Find its total surface area.

Answer (a)m²[1]

(b)The diagram shows a cuboid. Find its volume.

Answer (b)cm³[1]

(c)A rectangular water tank measures

150

cm by

80

cm by

60

cm. Find its capacity, in litres.

Answer (c)litres[2]

(d)The diagram shows a hollow metal pipe of length

15

cm. Its outer radius is

6

cm and its inner radius is

4.5

cm. Find the volume of metal in the pipe, correct to 3 significant figures.

Answer (d)cm³[2]

(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)The volume of a cylindrical pencil holder is

2000

cm³. Find its height,

h

, correct to 3 significant figures.

Answer (b)cm[2]

(c)The diagram shows a prism whose cross-section is a trapezium. The dashed line is perpendicular to the parallel sides. Find the total surface area of the prism.

Answer (c)cm²[3]

(a)The diagram shows a cylindrical pencil holder. Find its curved surface area, correct to 3 significant figures.

Answer (a)cm²[2]

(b)The total surface area of the closed cuboid is

552

m². Find the value of

h

Answer (b)m[2]

(c)(i)A container holds

3.75

m³. Express this volume in cm³.

Answer (c)(i)cm³[2]

(c)(ii)A box has a volume of

4\,500\,000

cm³. Express this volume in m³.

Answer (c)(ii)m³[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 12\,000\,000

cm³[2]

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

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

12 \text{ m}^3 = 12 \times 1\,000\,000 \text{ cm}^3

= 12\,000\,000

cm³

Question 2

Answer:

= 905

cm² (3 s.f.)[2]

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

= 2\pi(6)(18) + 2 \times \pi(6)^2

= 904.7786\ldots

= 905

cm² (3 s.f.)

Question 3

Answer:

h = 12

cm[2]

25 \times 10 \times h = 3000

250h = 3000

h = \dfrac{3000}{250}

h = 12

Question 4

Answer:

= 904

cm²[3]

\text{Cross-section} = 14 \times 10 - 8 \times 6

= 92

cm²

\text{Perimeter} = 14 + 4 + 8 + 6 + 6 + 10

= 48

\text{TSA} = 2 \times 92 + 48 \times 15

= 904

cm²

Question 5

(a)Answer:

= 288

m²[1]

\text{TSA} = 2(12 \times 6) + 2(12 \times 4) + 2(6 \times 4)

= 288

m²

(b)Answer:

= 180

cm³[1]

V = 7.5 \times 4 \times 6

= 180

cm³

(c)Answer:

= 720

litres[2]

V = 150 \times 80 \times 60

= 720\,000

cm³

\text{Capacity} = \dfrac{720000}{1000}

= 720

litres

(d)Answer:

= 742

cm³ (3 s.f.)[2]

V = \pi(6)^2(15) - \pi(4.5)^2(15)

= 742.2012\ldots

= 742

cm³ (3 s.f.)

Question 6

(a)Answer:

= 480

cm³[2]

\text{Area} = \dfrac{1}{2} \times (4 + 16) \times 6

= 60

cm²

V = 60 \times 8

= 480

cm³

(b)Answer:

= 13.0

cm (3 s.f.)[2]

\pi(7)^2 h = 2000

h = \dfrac{2000}{\pi(7)^2}

= 12.9922\ldots

= 13.0

cm (3 s.f.)

(c)Answer:

= 2464

cm²[3]

\text{Trapezium} = \dfrac{1}{2} \times (10 + 42) \times 12

= 312

cm²

\text{Perimeter} = 42 + 20 + 10 + 20

= 92

\text{TSA} = 2 \times 312 + 92 \times 20

= 2464

cm²

Question 7

(a)Answer:

= 377

cm² (3 s.f.)[2]

\text{CSA} = 2\pi r h

= 2\pi(10)(6)

= 376.9911\ldots

= 377

cm² (3 s.f.)

(b)Answer:

h = 7

m[2]

2(18 \times 6 + 18h + 6h) = 552

216 + 48h = 552

48h = 336

h = \dfrac{336}{48}

h = 7

(c)(i)Answer:

= 3\,750\,000

cm³[2]

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

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

3.75 \text{ m}^3 = 3.75 \times 1\,000\,000 \text{ cm}^3

= 3\,750\,000

cm³

(c)(ii)Answer:

= 4.5

m³[2]

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

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

4\,500\,000 \text{ cm}^3 = \dfrac{4\,500\,000}{1\,000\,000} \text{ m}^3

= 4.5

m³

Sec 1 G2 Maths Volume and surface area worksheet with answers

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

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)The diagram shows a cardboard box in the shape of a cuboid. Find its total surface area.

Answer (a)m²[1]

(b)The diagram shows a cuboid. Find its volume.

Answer (b)cm³[1]

(c)A rectangular water tank measures

150

cm by

80

cm by

60

cm. Find its capacity, in litres.

Answer (c)litres[2]

(d)The diagram shows a hollow metal pipe of length

15

cm. Its outer radius is

6

cm and its inner radius is

4.5

cm. Find the volume of metal in the pipe, correct to 3 significant figures.

Answer (d)cm³[2]

Answers and worked solutions

Question 1

Answer:

= 12\,000\,000

cm³[2]

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

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

12 \text{ m}^3 = 12 \times 1\,000\,000 \text{ cm}^3

= 12\,000\,000

cm³

Question 2

Answer:

= 905

cm² (3 s.f.)[2]

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

= 2\pi(6)(18) + 2 \times \pi(6)^2

= 904.7786\ldots

= 905

cm² (3 s.f.)

Question 3

Answer:

h = 12

cm[2]

25 \times 10 \times h = 3000

250h = 3000

h = \dfrac{3000}{250}

h = 12

Question 4

Answer:

= 904

cm²[3]

\text{Cross-section} = 14 \times 10 - 8 \times 6

= 92

cm²

\text{Perimeter} = 14 + 4 + 8 + 6 + 6 + 10

= 48

\text{TSA} = 2 \times 92 + 48 \times 15

= 904

cm²

Question 5

(a)Answer:

= 288

m²[1]

\text{TSA} = 2(12 \times 6) + 2(12 \times 4) + 2(6 \times 4)

= 288

m²

(b)Answer:

= 180

cm³[1]

V = 7.5 \times 4 \times 6

= 180

cm³

(c)Answer:

= 720

litres[2]

V = 150 \times 80 \times 60

= 720\,000

cm³

\text{Capacity} = \dfrac{720000}{1000}

= 720

litres

(d)Answer:

= 742

cm³ (3 s.f.)[2]

V = \pi(6)^2(15) - \pi(4.5)^2(15)

= 742.2012\ldots

= 742

cm³ (3 s.f.)

Question 6

(a)Answer:

= 480

cm³[2]

\text{Area} = \dfrac{1}{2} \times (4 + 16) \times 6

= 60

cm²

V = 60 \times 8

= 480

cm³

(b)Answer:

= 13.0

cm (3 s.f.)[2]

\pi(7)^2 h = 2000

h = \dfrac{2000}{\pi(7)^2}

= 12.9922\ldots

= 13.0

cm (3 s.f.)

(c)Answer:

= 2464

cm²[3]

\text{Trapezium} = \dfrac{1}{2} \times (10 + 42) \times 12

= 312

cm²

\text{Perimeter} = 42 + 20 + 10 + 20

= 92

\text{TSA} = 2 \times 312 + 92 \times 20

= 2464

cm²

Question 7

(a)Answer:

= 377

cm² (3 s.f.)[2]

\text{CSA} = 2\pi r h

= 2\pi(10)(6)

= 376.9911\ldots

= 377

cm² (3 s.f.)

(b)Answer:

h = 7

m[2]

2(18 \times 6 + 18h + 6h) = 552

216 + 48h = 552

48h = 336

h = \dfrac{336}{48}

h = 7

(c)(i)Answer:

= 3\,750\,000

cm³[2]

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

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

3.75 \text{ m}^3 = 3.75 \times 1\,000\,000 \text{ cm}^3

= 3\,750\,000

cm³

(c)(ii)Answer:

= 4.5

m³[2]

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

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

4\,500\,000 \text{ cm}^3 = \dfrac{4\,500\,000}{1\,000\,000} \text{ m}^3

= 4.5

m³