Sec 1 G1 Maths Volume and surface area worksheet with answers

A free Sec 1 G1 Maths worksheet on volume and surface area: 11 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 G1 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

The diagram shows a fish tank with no lid, in the shape of a cuboid. Find its total surface area (outside only).

Answerm²[1]

The diagram shows a wooden chest in the shape of a cuboid. Find its total surface area.

Answercm²[1]

The diagram shows a concrete step. All the corners of its cross-section are right angles. Find its volume.

Answerm³[2]

A box has a volume of

0.3

m³. Express this volume in cm³.

Answercm³[2]

A cuboid container measures

24

cm by

15

cm by

10

cm. Find its capacity, in litres.

Answerlitres[2]

The volume of the triangular prism is

504

m³. Find the value of

x

Answerm[2]

The diagram shows a prism with an L-shaped cross-section. All the corners of its cross-section are right angles. Find its volume.

Answercm³[2]

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.

Answercm²[3]

Section B

(a)The volume of the triangular prism is

300

cm³. Find the value of

x

Answer (a)cm[2]

(b)A rectangular aquarium measures

90

cm by

45

cm by

60

cm. It is empty, and water flows in from a tap at

5

litres per minute. Find the time, in minutes, taken to fill it completely.

Answer (b)minutes[3]

(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 swimming pool whose cross-section is a trapezium. The dashed line is perpendicular to the parallel sides. Find its volume.

Answer (b)cm³[2]

(c)A bottle holds

3.25

litres of water. Express this in cm³.

Answer (c)cm³[2]

(a)The diagram shows a metal tank with a lid in the shape of a cuboid. Find its total surface area.

Answer (a)m²[1]

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

Answer (b)m³[2]

(c)A bottle holds

3.25

litres of water. Express this in cm³.

Answer (c)cm³[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 251

m²[1]

\text{TSA} = 13 \times 7 + 2(13 \times 4) + 2(7 \times 4)

= 251

m²

Question 2

Answer:

= 588

cm²[1]

\text{TSA} = 2(24 \times 6) + 2(24 \times 5) + 2(6 \times 5)

= 588

cm²

Question 3

Answer:

= 1320

m³[2]

\text{Area} = 12 \times 9 - 7 \times 6

= 66

m²

V = 66 \times 20

= 1320

m³

Question 4

Answer:

= 300\,000

cm³[2]

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

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

0.3 \text{ m}^3 = 0.3 \times 1\,000\,000 \text{ cm}^3

= 300\,000

cm³

Question 5

Answer:

= 3.6

litres[2]

V = 24 \times 15 \times 10

= 3600

cm³

\text{Capacity} = \dfrac{3600}{1000}

= 3.6

litres

Question 6

Answer:

x = 9

m[2]

\text{Area} = \dfrac{1}{2} \times 14 \times 8

= 56

m²

56x = 504

x = \dfrac{504}{56}

x = 9

Question 7

Answer:

= 430

cm³[2]

\text{Area} = 9 \times 7 - 5 \times 4

= 43

cm²

V = 43 \times 10

= 430

cm³

Question 8

Answer:

= 1816

cm²[3]

\text{Trapezium} = \dfrac{1}{2} \times (10 + 28) \times 12

= 228

cm²

\text{Perimeter} = 28 + 15 + 10 + 15

= 68

\text{TSA} = 2 \times 228 + 68 \times 20

= 1816

cm²

Question 9

(a)Answer:

x = 12

cm[2]

\text{Area} = \dfrac{1}{2} \times 10 \times 5

= 25

cm²

25x = 300

x = \dfrac{300}{25}

x = 12

(b)Answer:

= 48.6

minutes[3]

V = 90 \times 45 \times 60

= 243\,000

cm³

\text{Capacity} = \dfrac{243000}{1000}

= 243

litres

\text{Time} = \dfrac{243}{5}

= 48.6

minutes

Question 10

(a)Answer:

= 1340

m²[1]

\text{TSA} = 2(25 \times 10) + 2(25 \times 12) + 2(10 \times 12)

= 1340

m²

(b)Answer:

= 336

cm³[2]

\text{Area} = \dfrac{1}{2} \times (3 + 11) \times 6

= 42

cm²

V = 42 \times 8

= 336

cm³

(c)Answer:

= 3250

cm³[2]

1 \text{ litre} = 1000 \text{ cm}^3

3.25 \text{ litres} = 3.25 \times 1000 \text{ cm}^3

= 3250

cm³

Question 11

(a)Answer:

= 348

m²[1]

\text{TSA} = 2(9 \times 8) + 2(9 \times 6) + 2(8 \times 6)

= 348

m²

(b)Answer:

= 896

m³[2]

\text{Area} = \dfrac{1}{2} \times (8 + 20) \times 8

= 112

m²

V = 112 \times 8

= 896

m³

(c)Answer:

= 3250

cm³[2]

1 \text{ litre} = 1000 \text{ cm}^3

3.25 \text{ litres} = 3.25 \times 1000 \text{ cm}^3

= 3250

cm³

Sec 1 G1 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 volume of the triangular prism is

300

cm³. Find the value of

x

Answer (a)cm[2]

(b)A rectangular aquarium measures

90

cm by

45

cm by

60

cm. It is empty, and water flows in from a tap at

5

litres per minute. Find the time, in minutes, taken to fill it completely.

Answer (b)minutes[3]

Answers and worked solutions

Question 1

Answer:

= 251

m²[1]

\text{TSA} = 13 \times 7 + 2(13 \times 4) + 2(7 \times 4)

= 251

m²

Question 2

Answer:

= 588

cm²[1]

\text{TSA} = 2(24 \times 6) + 2(24 \times 5) + 2(6 \times 5)

= 588

cm²

Question 3

Answer:

= 1320

m³[2]

\text{Area} = 12 \times 9 - 7 \times 6

= 66

m²

V = 66 \times 20

= 1320

m³

Question 4

Answer:

= 300\,000

cm³[2]

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

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

0.3 \text{ m}^3 = 0.3 \times 1\,000\,000 \text{ cm}^3

= 300\,000

cm³

Question 5

Answer:

= 3.6

litres[2]

V = 24 \times 15 \times 10

= 3600

cm³

\text{Capacity} = \dfrac{3600}{1000}

= 3.6

litres

Question 6

Answer:

x = 9

m[2]

\text{Area} = \dfrac{1}{2} \times 14 \times 8

= 56

m²

56x = 504

x = \dfrac{504}{56}

x = 9

Question 7

Answer:

= 430

cm³[2]

\text{Area} = 9 \times 7 - 5 \times 4

= 43

cm²

V = 43 \times 10

= 430

cm³

Question 8

Answer:

= 1816

cm²[3]

\text{Trapezium} = \dfrac{1}{2} \times (10 + 28) \times 12

= 228

cm²

\text{Perimeter} = 28 + 15 + 10 + 15

= 68

\text{TSA} = 2 \times 228 + 68 \times 20

= 1816

cm²

Question 9

(a)Answer:

x = 12

cm[2]

\text{Area} = \dfrac{1}{2} \times 10 \times 5

= 25

cm²

25x = 300

x = \dfrac{300}{25}

x = 12

(b)Answer:

= 48.6

minutes[3]

V = 90 \times 45 \times 60

= 243\,000

cm³

\text{Capacity} = \dfrac{243000}{1000}

= 243

litres

\text{Time} = \dfrac{243}{5}

= 48.6

minutes

Question 10

(a)Answer:

= 1340

m²[1]

\text{TSA} = 2(25 \times 10) + 2(25 \times 12) + 2(10 \times 12)

= 1340

m²

(b)Answer:

= 336

cm³[2]

\text{Area} = \dfrac{1}{2} \times (3 + 11) \times 6

= 42

cm²

V = 42 \times 8

= 336

cm³

(c)Answer:

= 3250

cm³[2]

1 \text{ litre} = 1000 \text{ cm}^3

3.25 \text{ litres} = 3.25 \times 1000 \text{ cm}^3

= 3250

cm³

Question 11

(a)Answer:

= 348

m²[1]

\text{TSA} = 2(9 \times 8) + 2(9 \times 6) + 2(8 \times 6)

= 348

m²

(b)Answer:

= 896

m³[2]

\text{Area} = \dfrac{1}{2} \times (8 + 20) \times 8

= 112

m²

V = 112 \times 8

= 896

m³

(c)Answer:

= 3250

cm³[2]

1 \text{ litre} = 1000 \text{ cm}^3

3.25 \text{ litres} = 3.25 \times 1000 \text{ cm}^3

= 3250

cm³