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GCSE · Geometry and Measures

4.14 Cylinders

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Which of these is the correct formula for the volume of a cylinder with radius r and height h?

A) V = 2 x π x r x h
B) V = π x r² x h
C) V = π x r x h²
D) V = 2 x π x r² + 2 x π x r x h

(Total for Question 1 is 1 mark)

Which of these is the correct formula for the curved surface area of a cylinder with radius r and height h?

A) A = π x r² x h
B) A = 2 x π x r²
C) A = 2 x π x r x h
D) A = π x r x h

(Total for Question 2 is 1 mark)

A cylinder has radius 4 cm and height 10 cm.
Calculate the volume of the cylinder. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 3 is 2 marks)

A cylinder has radius 3 cm and height 12 cm.
Calculate the curved surface area of the cylinder. Give your answer in terms of π.

Diagram NOT accurately drawn

(Total for Question 4 is 2 marks)

A cylindrical candle has diameter 8 cm and height 15 cm.
Diagram: cylinder labelled diameter 8 cm and height 15 cm.
Work out the total surface area of the candle. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 5 is 3 marks)

A cylindrical water butt has diameter 60 cm and height 1.2 m.
Diagram: cylinder labelled diameter 60 cm and height 1.2 m.
Calculate the volume of the water butt in cm^3. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 6 is 3 marks)

A cylindrical tin of paint has radius 7 cm and height 18 cm.
Diagram: cylinder labelled radius 7 cm and height 18 cm.

Diagram NOT accurately drawn

(a)Calculate the volume of the tin. Give your answer correct to the nearest whole number.(2)

(b)1 litre = 1000 cm^3. The tin is filled with paint to 90% of its volume.
Work out the volume of paint in the tin, in litres. Give your answer correct to 2 decimal places.(2)

(Total for Question 7 is 4 marks)

The volume of a cylinder is given by V = π x r² x h.
Which of these is the correct rearrangement to make h the subject?

A) h = V / (π x r²)
B) h = V x π x r²
C) h = (V/π) / r
D) h = V - π x r²

(Total for Question 8 is 1 mark)

A cylinder has radius 5 cm. The volume of the cylinder is 942 cm³, correct to 3 significant figures.
Diagram: cylinder labelled radius 5 cm, height h unknown.
Work out the height of the cylinder. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 9 is 3 marks)

A cylinder has height 30 cm. The volume of the cylinder is 15000 cm^3.
Diagram: cylinder labelled height 30 cm, radius r unknown.
Work out the radius of the cylinder. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 10 is 3 marks)

A trough is in the shape of a half-cylinder (a cylinder cut in half lengthways). The semicircular cross-section has radius 5 cm and the trough is 20 cm long.
Diagram: half-cylinder trough, semicircular cross-section radius 5 cm, length 20 cm.
Work out the volume of the trough. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 11 is 3 marks)

Cylinder A has radius 6 cm and height 12 cm. Cylinder B has radius 5 cm and height 16 cm.
Diagram: Cylinder A labelled radius 6 cm, height 12 cm; Cylinder B labelled radius 5 cm, height 16 cm.
Show that Cylinder A has the greater volume.

Diagram NOT accurately drawn

(Total for Question 12 is 4 marks)

A pipe is a hollow cylinder with outer radius 8 cm and inner radius 6 cm. The pipe is 50 cm long.
Diagram: hollow cylindrical pipe, outer radius 8 cm, inner radius 6 cm, length 50 cm.
Work out the volume of material used to make the pipe. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 13 is 4 marks)

Steel has a density of 7.8 g/cm^3. A solid cylindrical steel rod has radius 2 cm and length 25 cm.
Diagram: solid cylindrical rod labelled radius 2 cm and length 25 cm.
Work out the mass of the rod, in kilograms. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 14 is 4 marks)

Water is poured from a full cylindrical jug of radius 7 cm and height 18 cm into an empty cylindrical glass of radius 5 cm. All of the water fits into the glass, with none left over.
Diagram: cylindrical jug labelled radius 7 cm, height 18 cm; empty cylindrical glass labelled radius 5 cm.
Work out the height of the water in the glass. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 15 is 4 marks)

A solid cylinder of radius 4 cm and height 9 cm is melted down and recast, with no loss of metal, into a cuboid with a square base of side 6 cm.
Diagram: solid cylinder labelled radius 4 cm, height 9 cm; cuboid with square base side 6 cm, height h unknown.
Work out the height of the cuboid. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 16 is 4 marks)

A cylindrical can of soup has radius 3.5 cm and height 11 cm. The label covers the curved surface area only, with no overlap. Card for the label costs 0.8 pence per cm^2.
Diagram: cylindrical can labelled radius 3.5 cm and height 11 cm.
Work out the cost of the label. Give your answer to the nearest penny.

Diagram NOT accurately drawn

(Total for Question 17 is 3 marks)

A cylindrical water tank has radius 50 cm and height 1.4 m. The tank starts empty and is filled with water at a rate of 15000 cm³ per minute.
Diagram: cylindrical water tank labelled radius 50 cm and height 1.4 m.
Work out how long it takes to fill the tank completely. Give your answer in minutes, correct to the nearest minute.

Diagram NOT accurately drawn

(Total for Question 18 is 4 marks)

A cylindrical drum has diameter 1.4 m and height 2 m. Only the curved surface of the drum is to be painted. 1 litre of paint covers 6 m^2. Paint is sold only in 1 litre tins costing 12.50 pounds each.
Diagram: cylindrical drum labelled diameter 1.4 m and height 2 m.
Work out the total cost of the paint needed to paint the drum.

Diagram NOT accurately drawn

(Total for Question 19 is 4 marks)

A cylinder has radius 3 x √2 cm and height 5 cm.
Calculate the exact volume of the cylinder. Give your answer in terms of π.

(Total for Question 20 is 3 marks)

A composite solid is made from a cylinder of radius 4 cm and height 10 cm, with a cone of the same radius and height 6 cm attached on top.
Diagram: cylinder (radius 4 cm, height 10 cm) with a cone (same radius, height 6 cm) attached on top.
The volume of a cone = (1/3) x π x r² x h.
Work out the total volume of the solid. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 21 is 4 marks)

Mark scheme · 4.14 Cylinders

Question 1

B1 B cao
Answer: B

Question 2

B1 C cao
Answer: C

Question 3

M1 π x 4² x 10 oe (= 160pi)
A1 awrt 503 (units cm³)
Answer: 503 cm³ (3 s.f.)

Question 4

M1 2 x π x 3 x 12 oe
A1 72pi cao (units cm²)
Answer: 72pi cm²

Question 5

M1 radius 4 identified, curved surface area 2 x π x 4 x 15 (= 120pi) oe
M1 + 2 x π x 4² (= 32pi) for the two circular ends oe
A1 awrt 477.5 (units cm²)
Answer: 477.5 cm² (1 d.p.)

Question 6

M1 1.2 m converted to 120 cm
M1 π x 30² x 120 oe (radius 30 identified from diameter 60)
A1 awrt 339000 (units cm³)
Answer: 339000 cm³ (3 s.f.)

Question 7

(a) M1 π x 7² x 18 oe
(a) A1 awrt 2771 (units cm³)
(a) Answer: 2771 cm³
(b) M1 0.9 x their (a) ft
(b) A1 awrt 2.49 (units litres), converted using 1000 cm³ = 1 litre
(b) Answer: 2.49 litres

Question 8

B1 A cao
Answer: A

Question 9

M1 h = V / (π x r²) oe rearrangement
M1 942 / (π x 5²) oe substitution
A1 awrt 12.0 (units cm)
Answer: 12.0 cm (1 d.p.)

Question 10

M1 r² = V / (π x h) oe rearrangement
M1 15000 / (π x 30) oe substitution, then square root
A1 awrt 12.6 (units cm)
Answer: 12.6 cm (1 d.p.)

Question 11

M1 area of semicircle = 0.5 x π x 5² oe
M1 their area x 20 (length) oe
A1 awrt 785 (units cm³)
Answer: 785 cm³ (3 s.f.)

Question 12

M1 volume of A = π x 6² x 12 oe
A1 volume of A = 432pi = awrt 1357 (units cm³)
M1 volume of B = π x 5² x 16 oe
A1 volume of B = 400pi = awrt 1257 (units cm³), with conclusion that 1357 > 1257 so A is greater, cso
Answer: Volume of A = 1357.2 cm³, volume of B = 1256.6 cm³, so Cylinder A has the greater volume.

Question 13

M1 8² - 6² (= 28), area of cross-section of the material oe
M1 π x 28 oe (= 28pi)
M1 their area x 50 oe (= 1400pi)
A1 awrt 4400 (units cm³)
Answer: 4400 cm³ (3 s.f.)

Question 14

M1 volume = π x 2² x 25 oe (= 100pi)
M1 mass = 7.8 x their volume oe
M1 convert grams to kilograms (divide by 1000)
A1 awrt 2.45 (units kg)
Answer: 2.45 kg (3 s.f.)

Question 15

M1 volume of jug = π x 7² x 18 oe (= 882pi)
M1 h = volume / (π x 5²) oe rearrangement
M1 882pi / (π x 25) oe substitution
A1 awrt 35.3 (units cm)
Answer: 35.3 cm (1 d.p.)

Question 16

M1 volume of cylinder = π x 4² x 9 oe (= 144pi)
M1 volume of cuboid = 6 x 6 x h oe, set equal to volume of cylinder
M1 h = their 144pi / 36 oe
A1 awrt 12.6 (units cm)
Answer: 12.6 cm (1 d.p.)

Question 17

M1 CSA = 2 x π x 3.5 x 11 oe (= 77pi)
M1 cost = their CSA x 0.8 oe
A1 awrt 194 pence (or 1.94 pounds), correctly rounded to the nearest penny
Answer: 194 pence (1.94 pounds)

Question 18

M1 1.4 m converted to 140 cm
M1 volume = π x 50² x 140 oe
M1 time = their volume / 15000 oe
A1 awrt 73 (units minutes)
Answer: 73 minutes (nearest minute)

Question 19

M1 radius 0.7 m identified, CSA = 2 x π x 0.7 x 2 oe (= 2.8pi)
M1 litres needed = their CSA / 6 oe (= awrt 1.47)
B1 rounds up to 2 whole tins needed (since only whole tins can be bought)
A1 25.00 pounds cao (= 2 x 12.50)
Answer: 25.00 pounds

Question 20

M1 (3 x √2)² = 18 oe
M1 π x 18 x 5 oe
A1 90pi cao (units cm³)
Answer: 90pi cm³

Question 21

M1 volume of cylinder = π x 4² x 10 oe (= 160pi)
M1 volume of cone = (1/3) x π x 4² x 6 oe (= 32pi)
M1 total = their cylinder + their cone oe (= 192pi)
A1 awrt 603 (units cm³)
Answer: 603 cm³ (3 s.f.)

Cylinders - Worksheets, Questions and Revision

4.14 Cylinders

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21