Perimeter, Area, Surface Area and Volume - Worksheets, Questions and Revision

20 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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13+ · Mathematics

CE.M11 Perimeter, Area, Surface Area and Volume

ISEB CE ISEB CE 13+ Mathematics · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A rectangular photo frame has length 18 cm and width 12 cm. Calculate the perimeter of the frame.

(Total for Question 1 is 1 mark)

A square patio slab has a side length of 11 cm. Calculate the area of the slab.

(Total for Question 2 is 2 marks)

A square rug has a side length of 6.5 m. Calculate the perimeter of the rug.

(Total for Question 3 is 2 marks)

A rectangular lawn has length 8 m and width 5 m. Calculate the area of the lawn.

(Total for Question 4 is 2 marks)

A triangular flag has a base of 10 cm and a perpendicular height of 6 cm. Calculate the area of the flag.

(Total for Question 5 is 2 marks)

A patio is tiled with regular hexagonal paving slabs of side length 4.5 cm. Calculate the perimeter of one hexagonal slab.

(Total for Question 6 is 3 marks)

A cuboid-shaped storage box measures 6 cm by 4 cm by 3 cm. Calculate the volume of the box.

(Total for Question 7 is 3 marks)

A cube-shaped gift box has an edge length of 5 cm. Calculate the total surface area of the box.

(Total for Question 8 is 3 marks)

A parallelogram-shaped flower bed has a base of 12 m. The perpendicular height is 5.5 m and the slanted side is 6 m.

(a)Calculate the area of the flower bed.(3)

(Total for Question 9 is 3 marks)

A trapezium-shaped decking area has parallel sides of length 9 m and 15 m. The perpendicular distance between the parallel sides is 5 m. Calculate the area of the decking.

(Total for Question 10 is 3 marks)

A circular pond has a diameter of 10 m. Calculate the circumference of the pond, giving your answer to 3 significant figures.

(Total for Question 11 is 2 marks)

A circular flower bed has a diameter of 14 m. Calculate the area of the flower bed, giving your answer to 3 significant figures.

(Total for Question 12 is 3 marks)

A rectangular garden measuring 10 m by 7 m has a rectangular corner cut out, measuring 4 m by 3 m, removed from one corner, making an L-shaped lawn.

(a)Calculate the area of the L-shaped lawn.(3)

(b)Calculate the perimeter of the L-shaped lawn.(3)

(Total for Question 13 is 6 marks)

A cuboid box measures 12 cm by 8 cm by 5 cm.

(a)Calculate the volume of the box.(2)

(b)Calculate the total surface area of the box.(3)

(Total for Question 14 is 5 marks)

A triangular prism has a cross-section which is a right-angled triangle with base 6 cm and height 4 cm. The length of the prism is 15 cm. Calculate the volume of the prism.

(Total for Question 15 is 3 marks)

A semicircular flower bed has a diameter of 12 m. Calculate the perimeter of the flower bed (the curved edge plus the straight edge), giving your answer to 3 significant figures.

(Total for Question 16 is 3 marks)

A drainage channel has a cross-section in the shape of a trapezium with parallel sides of 4 cm and 10 cm, and a perpendicular height of 5 cm. The channel is 20 cm long. Calculate the volume of the channel.

(Total for Question 17 is 4 marks)

A cylindrical drum has a radius of 5 cm and a height of 12 cm.

(a)Calculate the volume of the drum, giving your answer to 3 significant figures.(2)

(b)Calculate the total surface area of the drum, giving your answer to 3 significant figures.(4)

(Total for Question 18 is 6 marks)

A pyramid has a square base of side 6 cm and a vertical height of 10 cm. Given that the volume of a pyramid = (1/3) x base area x height, calculate the volume of the pyramid.

(Total for Question 19 is 3 marks)

An athletics running track is made from a rectangle measuring 40 m by 20 m, with a semicircular end of diameter 20 m attached to each of the two short sides, so that the two semicircles together form one full circle.

(a)Calculate the total perimeter of the running track, giving your answer to the nearest whole number of metres.(4)

(b)Calculate the total area enclosed by the running track, giving your answer to the nearest whole number of square metres.(4)

(Total for Question 20 is 8 marks)

Mark scheme · CE.M11 Perimeter, Area, Surface Area and Volume

Question 1

B1 60 cm cao
Answer: 60 cm

Question 2

M1 11 x 11 oe
A1 121 cm² cao
Answer: 121 cm²

Question 3

M1 4 x 6.5 oe
A1 26 m cao
Answer: 26 m

Question 4

M1 8 x 5 oe
A1 40 m² cao
Answer: 40 m²

Question 5

M1 0.5 x 10 x 6 oe
A1 30 cm² cao
Answer: 30 cm²

Question 6

B1 recognises a regular hexagon has 6 equal sides
M1 6 x 4.5
A1 27 cm cao
Answer: 27 cm

Question 7

M1 6 x 4 oe (=24)
M1 24 x 3
A1 72 cm³ cao
Answer: 72 cm³

Question 8

M1 area of one face = 5 x 5 (=25)
M1 25 x 6
A1 150 cm² cao
Answer: 150 cm²

Question 9

(a) M1 identifies 5.5 m as the perpendicular height needed, not the 6 m slant side, oe
(a) M1 12 x 5.5
(a) A1 66 m² cao
(a) Answer: 66 m²

Question 10

M1 9 + 15 oe (=24)
M1 0.5 x 24 x 5 (ft)
A1 60 m² cao
Answer: 60 m²

Question 11

M1 π x 10 oe
A1 31.4 m (awrt 31.4)
Answer: 31.4 m

Question 12

M1 radius = 14 / 2 = 7 m
M1 π x 7² oe
A1 154 m² (awrt 154)
Answer: 154 m²

Question 13

(a) M1 area of full rectangle = 10 x 7 (=70)
(a) M1 area removed = 4 x 3 (=12)
(a) A1 58 m² cao
(a) Answer: 58 m²
(b) M1 identifies all six edge lengths of the L-shape (10, 4, 4, 3, 6, 7), oe
(b) M1 adds all six edge lengths
(b) A1 34 m cao
(b) Answer: 34 m

Question 14

(a) M1 12 x 8 x 5
(a) A1 480 cm³ cao
(a) Answer: 480 cm³
(b) M1 identifies the three distinct face areas: 12x8 (=96), 12x5 (=60), 8x5 (=40)
(b) M1 (96+60+40) x 2
(b) A1 392 cm² cao
(b) Answer: 392 cm²

Question 15

M1 area of triangle = 0.5 x 6 x 4 (=12)
M1 12 x 15
A1 180 cm³ cao
Answer: 180 cm³

Question 16

M1 curved length = 0.5 x π x 12 oe (=18.8)
M1 adds the straight edge of 12 m
A1 30.8 m (awrt 30.8)
Answer: 30.8 m

Question 17

M1 recognises volume = cross-sectional area x length, oe
M1 cross-sectional area = 0.5 x (4+10) x 5 (=35)
M1 35 x 20
A1 700 cm³ cao
Answer: 700 cm³

Question 18

(a) M1 π x 5² x 12 oe
(a) A1 942 cm³ (awrt 942)
(a) Answer: 942 cm³
(b) M1 curved surface area = 2 x π x 5 x 12 oe (=377)
(b) M1 area of the two circular ends = 2 x π x 5² oe (=157)
(b) M1 adds the curved surface area and the two ends
(b) A1 534 cm² (awrt 534)
(b) Answer: 534 cm²

Question 19

M1 base area = 6 x 6 (=36)
M1 (1/3) x 36 x 10
A1 120 cm³ cao
Answer: 120 cm³

Question 20

(a) M1 2 x 40 (the two straight sides, =80)
(a) M1 circumference of the full circle formed by the two semicircular ends = π x 20 oe (=62.8)
(a) M1 adds the straight and curved lengths
(a) A1 143 m cao (awrt 143)
(a) Answer: 143 m
(b) M1 area of rectangle = 40 x 20 (=800)
(b) M1 area of full circle formed by the two semicircular ends = π x 10² oe (=314)
(b) M1 adds the rectangle and circle areas
(b) A1 1114 m² cao (awrt 1114)
(b) Answer: 1114 m²

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