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4.14D Cylinders: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Formulae You May Need

Revision Library formulae reminder, styled on Edexcel 1MA1 formulae-sheet conventions; wording is original.

Volume of a cylinder = pi x r^2 x h

Curved surface area of a cylinder = 2 x pi x r x h

Total surface area of a cylinder = 2 x pi x r x h + 2 x pi x r^2 = 2 x pi x r x (h + r)

Note: on the Edexcel formulae sheet, the volume formula for a cylinder is given. The surface area formulae are not given and should be recalled or derived.

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 1 is 2 marks)

A cylinder has diameter 10 cm and height 6 cm. Calculate the volume of the cylinder. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 2 is 2 marks)

A cylinder has radius 3 cm and height 8 cm. Calculate the curved surface area 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 2 cm and height 5 cm. Calculate the total surface area of the cylinder (the curved surface plus the two circular ends). Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 4 is 3 marks)

A cylinder has radius 1.5 cm and height 12 cm. Calculate the volume of the cylinder. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 5 is 2 marks)

A cylindrical tin has radius 5 cm and height 15 cm. Work out the volume of the tin. Give your answer in litres, correct to 3 significant figures (1000 cm³ = 1 litre).

Diagram NOT accurately drawn

(Total for Question 6 is 3 marks)

A cylinder has volume 500 cm³ and radius 4 cm. Rearrange V = π x r² x h to make h the subject, then work out the height of the cylinder. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 7 is 3 marks)

A cylinder has volume 942 cm³ (to the nearest whole number) and height 12 cm. Rearrange V = π x r² x h to make r the subject, then work out the radius of the cylinder. Give your answer correct to 1 decimal place.

Diagram NOT accurately drawn

(Total for Question 8 is 3 marks)

A cylinder has curved surface area 220 cm² and radius 5 cm. Rearrange CSA = 2 x π x r x h to make h the subject, then work out the height of the cylinder. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 9 is 3 marks)

A cylinder has volume 2000 cm³ and height 25 cm. Work out the diameter of the cylinder. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 10 is 3 marks)

A cylindrical candle has radius 3.5 cm and height 9 cm. Calculate the volume of wax needed to make the candle. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 11 is 2 marks)

Mrs Okafor's cylindrical water butt has radius 30 cm and height 80 cm. Work out the capacity of the water butt in litres, correct to 3 significant figures (1 cm³ = 1 ml, 1000 ml = 1 litre).

Diagram NOT accurately drawn

(Total for Question 12 is 3 marks)

A cylinder has radius 6 cm and height 14 cm. Calculate the total surface area of the cylinder. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 13 is 3 marks)

A cylinder has total surface area 300 cm² and radius 4 cm. Work out the height of the cylinder. Give your answer correct to 3 significant figures.

Diagram NOT accurately drawn

(Total for Question 14 is 3 marks)

Yasmin needs 250 ml of soup for a recipe. She has one unopened tin of soup shaped like a cylinder, with internal radius 3.5 cm and internal height 11 cm. Determine whether the tin contains enough soup for the recipe. Show your working and state how much soup (in ml) would be left over, or how much extra Yasmin would need.

Diagram NOT accurately drawn

(Total for Question 15 is 4 marks)

Cylinder A has radius 4 cm and height 9 cm. Cylinder B has radius 6 cm and height x cm. Cylinder A and Cylinder B have the same volume. Work out the value of x.

Diagram NOT accurately drawn

(Total for Question 16 is 3 marks)

Priya, a silversmith, melts down a solid cylindrical silver bar of radius 2 cm and height 9 cm. She recasts all of the silver into 6 identical smaller solid cylinders, each of radius 1 cm. Work out the height of each smaller cylinder.

Diagram NOT accurately drawn

(Total for Question 17 is 4 marks)

Mr Jankowski is filling a cylindrical paddling pool in his garden. The pool has diameter 6 m and he fills it to a depth of 1.4 m. Water flows from his hose at a rate of 500 litres per minute. Work out how long it will take to fill the pool to this depth, giving your answer to the nearest minute.

Diagram NOT accurately drawn

(Total for Question 18 is 5 marks)

Leon needs to paint 10 identical cylindrical oil drums for use as planters. Each drum has radius 0.5 m and height 1.2 m, and needs painting all over (the curved surface and both circular ends). One tin of paint covers 4 m² and costs 6.50 pounds. Tins cannot be shared between jobs, so Leon must buy whole tins. Work out the total cost of the paint Leon needs to buy.

Diagram NOT accurately drawn

(Total for Question 19 is 5 marks)

Declan's cylindrical water butt has radius 25 cm and currently holds water to a depth of 40 cm. He uses a cylindrical bucket of radius 10 cm and height 30 cm to empty the butt, filling the bucket completely each time. Work out the greatest number of full buckets Declan can fill, and work out how much water (in litres, to 3 significant figures) is left in the butt afterwards.

Diagram NOT accurately drawn

(Total for Question 20 is 5 marks)

A cylinder has radius r cm and height h cm, where r and h are both greater than zero. The curved surface area of the cylinder, in cm², is numerically equal to the volume of the cylinder, in cm^3. Show that r = 2, whatever the value of h.

Diagram NOT accurately drawn

(Total for Question 21 is 4 marks)

Two similar cylinders, cylinder P and cylinder Q, have volumes in the ratio 8:27 (P smaller, Q larger). The curved surface area of cylinder P is 40pi cm^2. Work out the curved surface area of cylinder Q.

Diagram NOT accurately drawn

(Total for Question 22 is 4 marks)

Mark scheme · 4.14D Cylinders: Fluency and Exam Drill

Question 1

M1 correct substitution into V = π x r² x h, e.g. π x 4² x 10 (oe)
A1 awrt 503 cm³ (cao)
Answer: 503 cm³ (3 s.f.)

Question 2

M1 radius = 5 identified and correct substitution into V = π x r² x h, e.g. π x 5² x 6 (oe)
A1 awrt 471 cm³ (cao)
Answer: 471 cm³ (3 s.f.)

Question 3

M1 correct substitution into CSA = 2 x π x r x h, e.g. 2 x π x 3 x 8 (oe)
A1 awrt 151 cm² (cao)
Answer: 151 cm² (3 s.f.)

Question 4

M1 curved surface area = 2 x π x 2 x 5 (= 20pi) (oe)
M1 area of the two circular ends = 2 x π x 2² (= 8pi) (oe)
A1 awrt 88.0 cm² (cao)
Answer: 88.0 cm² (3 s.f.)

Question 5

M1 correct substitution into V = π x r² x h, e.g. π x 1.5² x 12 (oe)
A1 awrt 84.8 cm³ (cao)
Answer: 84.8 cm³ (3 s.f.)

Question 6

M1 correct substitution into V = π x r² x h, e.g. π x 5² x 15 (oe)
M1 dividing their volume in cm³ by 1000 (ft)
A1 awrt 1.18 litres (cao)
Answer: 1.18 litres (3 s.f.)

Question 7

M1 h = V / (π x r²) stated or used, oe
M1 correct substitution, e.g. 500 / (π x 4²) (oe)
A1 awrt 9.95 cm (cao)
Answer: h = 9.95 cm (3 s.f.)

Question 8

M1 r = √V / (&π; x h) stated or used, oe
M1 correct substitution, e.g. √942 / (&π; x 12) (oe)
A1 awrt 5.0 cm (cao)
Answer: r = 5.0 cm (1 d.p.)

Question 9

M1 h = CSA / (2 x π x r) stated or used, oe
M1 correct substitution, e.g. 220 / (2 x π x 5) (oe)
A1 awrt 7.00 cm (cao)
Answer: h = 7.00 cm (3 s.f.)

Question 10

M1 r = √V / (&π; x h) stated or used, oe
M1 correct substitution and doubling to find the diameter, e.g. 2 x √2000 / (&π; x 25) (oe)
A1 awrt 10.1 cm (cao)
Answer: diameter = 10.1 cm (3 s.f.)

Question 11

M1 correct substitution into V = π x r² x h, e.g. π x 3.5² x 9 (oe)
A1 awrt 346 cm³ (cao)
Answer: 346 cm³ (3 s.f.)

Question 12

M1 correct substitution into V = π x r² x h, e.g. π x 30² x 80 (oe)
M1 converting their volume in cm³ to litres (ft)
A1 awrt 226 litres (cao)
Answer: 226 litres (3 s.f.)

Question 13

M1 curved surface area = 2 x π x 6 x 14 (= 168pi) (oe)
M1 area of the two circular ends = 2 x π x 6² (= 72pi) (oe)
A1 awrt 754 cm² (cao)
Answer: 754 cm² (3 s.f.)

Question 14

M1 (h + r) = TSA / (2 x π x r), e.g. 300 / (2 x π x 4) (oe)
M1 (h + r) = awrt 11.9 (ft)
A1 awrt 7.94 cm (cao), from subtracting r = 4 from their (h + r)
Answer: h = 7.94 cm (3 s.f.)

Question 15

M1 correct substitution into V = π x r² x h, e.g. π x 3.5² x 11 (oe)
A1 awrt 423 cm³ (or ml) (cao)
M1 comparing their volume to 250 ml
A1 correct conclusion that there is enough soup, with awrt 173 ml left over (ft)
Answer: Yes; the tin holds awrt 423 ml, which is enough, with awrt 173 ml left over.

Question 16

M1 π x 4² x 9 = π x 6² x x, oe (equating the two volumes)
M1 144 = 36x, or equivalent correct simplification
A1 x = 4 cao
Answer: x = 4

Question 17

M1 volume of original bar = π x 2² x 9 (= 36pi) (oe)
M1 volume of one small cylinder = π x 1² x h, oe, in terms of h
M1 6 x π x 1² x h = 36pi, oe (equating total volume of 6 small cylinders to original volume)
A1 h = 6 cm cao
Answer: h = 6 cm

Question 18

M1 radius = 3 m identified
M1 correct substitution into V = π x r² x h, e.g. π x 3² x 1.4 (oe)
M1 converting their volume in m³ to litres, using 1 m³ = 1000 litres (ft)
M1 dividing their volume in litres by 500 (ft)
A1 79 minutes cao (accept awrt 79 minutes, or equivalent statement such as 1 hour 19 minutes)
Answer: 79 minutes (awrt), i.e. 1 hour 19 minutes

Question 19

M1 correct substitution into TSA = 2 x π x r x (h + r), e.g. 2 x π x 0.5 x 1.7 (oe)
A1 TSA of one drum = awrt 5.34 m² (cao)
M1 multiplying their TSA by 10 (ft)
M1 dividing their total area by 4 and rounding up to a whole number of tins (ft)
A1 91 pounds cao (from 14 tins x 6.50 pounds)
Answer: 91 pounds

Question 20

M1 volume of water in butt = π x 25² x 40 (= 25000pi) (oe)
M1 volume of bucket = π x 10² x 30 (= 3000pi) (oe)
M1 dividing their two volumes and rounding down to a whole number of buckets (ft)
A1 8 full buckets cao
A1 awrt 3.14 litres remaining (cao)
Answer: 8 full buckets; awrt 3.14 litres remain

Question 21

M1 setting curved surface area equal to volume: 2 x π x r x h = π x r² x h, oe
M1 dividing both sides by π x r x h (valid since r > 0 and h > 0)
B1 correct statement that h cancels from both sides, so the result is independent of h
A1 r = 2 shown, cso
Answer: r = 2 (shown, for any h > 0)

Question 22

M1 linear scale factor = cube root(8/27) = 2/3, oe
M1 area scale factor = (2/3)² = 4/9, oe
M1 setting up 40pi / (4/9) or equivalent correct method to scale the given area up to cylinder Q
A1 90pi cm² (oe, accept awrt 283 cm²), cao
Answer: 90pi cm² (awrt 283 cm²)

Cylinders: Fluency and Exam Drill - Worksheets, Questions and Revision

4.14D Cylinders: Fluency and Exam Drill

Formulae You May Need

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

Question 22