Sec 2 G1 Maths Prisms and cylinders worksheet with answers

A free Sec 2 G1 Maths worksheet on prisms and cylinders: 9 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 2 G1 Maths worksheet: Prisms and cylinders

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 shoebox in the shape of a cuboid. Find its volume.

Answercm³[1]

The diagram shows a cylindrical pencil holder. Find its volume, leaving your answer in terms of

\pi

Answercm³[2]

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

Answerm³[2]

The diagram shows a triangular prism. Its cross-section is a right-angled triangle. Find its total surface area.

Answercm²[3]

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

Answerm²[3]

The diagram shows a cylindrical candle. Find its curved surface area, correct to 3 significant figures.

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 volume of the triangular prism is

504

m³. Find the value of

x

Answer (b)m[2]

(c)The diagram shows a cylindrical pencil holder. Find its volume, leaving your answer in terms of

\pi

Answer (c)cm³[2]

(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 cylindrical tin, open at the top. Find its total surface area, correct to 3 significant figures.

Answer (b)cm²[2]

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

Answer (c)m³[2]

(a)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 (a)m²[3]

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

Answer (b)cm²[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 21

cm³[1]

V = 3.5 \times 3 \times 2

= 21

cm³

Question 2

Answer:

= 600\pi

cm³[2]

V = \pi r^2 h

= \pi(10)^2(6)

= 600\pi

cm³

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:

= 132

cm²[3]

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

= 6

cm²

\text{Perimeter} = 3 + 4 + 5

= 12

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

= 132

cm²

Question 5

Answer:

= 648

m²[3]

\text{Triangle} = \dfrac{1}{2} \times 9 \times 12

= 54

m²

\text{Perimeter} = 9 + 12 + 15

= 36

\text{TSA} = 2 \times 54 + 36 \times 15

= 648

m²

Question 6

Answer:

= 320

cm² (3 s.f.)[3]

r = \dfrac{17}{2}

= 8.5

\text{CSA} = 2\pi r h

= 2\pi(8.5)(6)

= 320.4424\ldots

= 320

cm² (3 s.f.)

Question 7

(a)Answer:

= 288

m²[1]

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

= 288

m²

(b)Answer:

x = 9

m[2]

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

= 56

m²

56x = 504

x = \dfrac{504}{56}

x = 9

(c)Answer:

= 72\pi

cm³[2]

r = \dfrac{6}{2}

= 3

V = \pi r^2 h

= \pi(3)^2(8)

= 72\pi

cm³

Question 8

(a)Answer:

= 342

m²[1]

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

= 342

m²

(b)Answer:

= 518

cm² (3 s.f.)[2]

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

= 2\pi(5)(14) + \pi(5)^2

= 518.3627\ldots

= 518

cm² (3 s.f.)

(c)Answer:

= 600

m³[2]

\text{Area} = \dfrac{1}{2} \times (5 + 15) \times 5

= 50

m²

V = 50 \times 12

= 600

m³

Question 9

(a)Answer:

= 1072

m²[3]

\text{Trapezium} = \dfrac{1}{2} \times (6 + 18) \times 8

= 96

m²

\text{Perimeter} = 18 + 10 + 6 + 10

= 44

\text{TSA} = 2 \times 96 + 44 \times 20

= 1072

m²

(b)Answer:

= 88.0

cm² (3 s.f.)[3]

r = \dfrac{4}{2}

= 2

\text{CSA} = 2\pi r h

= 2\pi(2)(7)

= 87.9645\ldots

= 88.0

cm² (3 s.f.)

Sec 2 G1 Maths Prisms and cylinders 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 volume of the triangular prism is

504

m³. Find the value of

x

Answer (b)m[2]

(c)The diagram shows a cylindrical pencil holder. Find its volume, leaving your answer in terms of

\pi

Answer (c)cm³[2]

Answers and worked solutions

Question 1

Answer:

= 21

cm³[1]

V = 3.5 \times 3 \times 2

= 21

cm³

Question 2

Answer:

= 600\pi

cm³[2]

V = \pi r^2 h

= \pi(10)^2(6)

= 600\pi

cm³

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:

= 132

cm²[3]

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

= 6

cm²

\text{Perimeter} = 3 + 4 + 5

= 12

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

= 132

cm²

Question 5

Answer:

= 648

m²[3]

\text{Triangle} = \dfrac{1}{2} \times 9 \times 12

= 54

m²

\text{Perimeter} = 9 + 12 + 15

= 36

\text{TSA} = 2 \times 54 + 36 \times 15

= 648

m²

Question 6

Answer:

= 320

cm² (3 s.f.)[3]

r = \dfrac{17}{2}

= 8.5

\text{CSA} = 2\pi r h

= 2\pi(8.5)(6)

= 320.4424\ldots

= 320

cm² (3 s.f.)

Question 7

(a)Answer:

= 288

m²[1]

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

= 288

m²

(b)Answer:

x = 9

m[2]

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

= 56

m²

56x = 504

x = \dfrac{504}{56}

x = 9

(c)Answer:

= 72\pi

cm³[2]

r = \dfrac{6}{2}

= 3

V = \pi r^2 h

= \pi(3)^2(8)

= 72\pi

cm³

Question 8

(a)Answer:

= 342

m²[1]

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

= 342

m²

(b)Answer:

= 518

cm² (3 s.f.)[2]

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

= 2\pi(5)(14) + \pi(5)^2

= 518.3627\ldots

= 518

cm² (3 s.f.)

(c)Answer:

= 600

m³[2]

\text{Area} = \dfrac{1}{2} \times (5 + 15) \times 5

= 50

m²

V = 50 \times 12

= 600

m³

Question 9

(a)Answer:

= 1072

m²[3]

\text{Trapezium} = \dfrac{1}{2} \times (6 + 18) \times 8

= 96

m²

\text{Perimeter} = 18 + 10 + 6 + 10

= 44

\text{TSA} = 2 \times 96 + 44 \times 20

= 1072

m²

(b)Answer:

= 88.0

cm² (3 s.f.)[3]

r = \dfrac{4}{2}

= 2

\text{CSA} = 2\pi r h

= 2\pi(2)(7)

= 87.9645\ldots

= 88.0

cm² (3 s.f.)