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KS3 · Geometry and Measures

KS3.M-G2 Geometry: Area, Perimeter and Volume

AQA AQA KS3 Mathematics · Calculator allowed · about 90 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A rectangular school playing field is being measured for a sports day.

(a)State the correct unit for the area of the field.(1)

A) m
B) m²
C) m³
D) cm

(b)The field is 9 m long and 3.5 m wide. Calculate the perimeter of the field.(2)

A rectangular whiteboard measures 1.6 m by 0.9 m.

(a)Calculate the area of the whiteboard.(2)

(b)A different rectangular tile has an area of 18 cm² and a length of 6 cm. Work out the width of the tile.(2)

A triangular sail has a base of 12 cm and a perpendicular height of 5 cm. Calculate the area of the sail.

Diagram NOT accurately drawn

(2)

A parallelogram-shaped tile has a base of 8.4 cm and a perpendicular height of 5 cm. Calculate the area of the tile.

Diagram NOT accurately drawn

(2)

The diagram shows the floor plan of an L-shaped garden. All lengths are in metres. The bottom edge is 10 m, the lower-right edge is 4 m, the top-left edge is 4 m and the left edge is 7 m. Two edges are unlabelled: p (an inner horizontal edge) and q (an inner vertical edge). All angles are right angles.

Diagram NOT accurately drawn

(a)Find the lengths of the edges marked p and q.(2)

(b)Work out the perimeter of the garden.(2)

(c)Work out the area of the garden.(3)

A trapezium-shaped flower bed has parallel sides of length 7 m and 11 m, and a perpendicular height of 4 m between them. Calculate the area of the flower bed.

Diagram NOT accurately drawn

(2)

Give your answers to 3 significant figures.

(a)A circular pond has a radius of 6 m. Calculate its circumference.(2)

(b)A circular tabletop has a diameter of 15 cm. Calculate its circumference.(2)

Use the π button on your calculator. Give your answers to 3 significant figures.

Diagram NOT accurately drawn

(a)A circular mirror has a radius of 4.5 cm. Calculate its area.(2)

(b)A window is made from a rectangle 0.8 m wide and 1.2 m tall, with a semicircle of radius 0.4 m fitted on top of it (see diagram). Calculate the total area of the window.(3)

Unit conversions.

(a)Convert 3.2 m² to cm^2.(2)

(b)A small tile has an area of 250 mm^2. Convert this to cm^2.(2)

A cuboid box has length 8 cm, width 5 cm and height 3 cm. Calculate the volume of the box.

Diagram NOT accurately drawn

(2)

A prism has a triangular cross-section with base 5 cm and perpendicular height 4 cm. The length of the prism is 9 cm. Calculate the volume of the prism.

Diagram NOT accurately drawn

(3)

A cuboid has length 6 cm, width 4 cm and height 3 cm. Calculate the total surface area of the cuboid.

Diagram NOT accurately drawn

(3)

A rectangular room measures 4.2 m by 3.5 m. New carpet costs 18.50 pounds per m^2. Calculate the total cost of carpeting the room.

(3)

The L-shaped garden from Question 5 has an area of 52 m^2. It is covered with a uniform layer of gravel 0.1 m deep. Calculate the volume of gravel needed.

(3)

A fish tank in the shape of a cuboid has internal dimensions 50 cm by 30 cm by 25 cm. Calculate the capacity of the tank in litres.

(3)

A quarter-circle flower bed has a radius of 3.5 m (a sector with angle 90 degrees). Give your answers to 3 significant figures.

Diagram NOT accurately drawn

(a)Calculate the arc length of the flower bed's curved edge.(2)

(b)Calculate the area of the flower bed.(2)

A wall measures 4.5 m long and 2.6 m high. It contains one rectangular window measuring 1.2 m by 1 m and one rectangular door measuring 0.9 m by 2 m. One litre of paint covers 12 m^2. Paint is sold only in 2.5-litre tins.

Diagram NOT accurately drawn

(a)Calculate the area of the wall that needs to be painted (the wall area minus the window and the door).(2)

(b)Calculate the minimum number of 2.5-litre tins of paint needed. Show your working.(2)

A prism has a right-angled triangular cross-section with the two shorter sides measuring 3 cm and 4 cm (hypotenuse 5 cm). The length of the prism is 12 cm. Calculate the total surface area of the prism.

Diagram NOT accurately drawn

(4)

A cuboid has a square base of side x cm and height (x+3) cm. Its volume is 100 cm^3. By trial and improvement, find the value of x correct to 1 decimal place. Show at least two trials.

(3)

A cylindrical water butt has a diameter of 60 cm and a height of 1.2 m.

Diagram NOT accurately drawn

(a)Calculate the volume of the water butt in m³, giving your answer to 3 significant figures.(3)

(b)Convert your answer to part (a) into litres, giving your answer to 3 significant figures.(2)

Mark scheme · KS3.M-G2 Geometry: Area, Perimeter and Volume

Question 1

(a) B1 B) m² selected
(a) Answer: B) m²
(b) M1 2*(9+3.5) oe, or 9+9+3.5+3.5
(b) A1 25 m cao
(b) Answer: 25 m

Question 2

(a) M1 1.6*0.9 oe
(a) A1 1.44 m² cao
(a) Answer: 1.44 m²
(b) M1 18/6 oe
(b) A1 3 cm cao
(b) Answer: 3 cm

Question 3

M1 0.5*12*5 oe
A1 30 cm² cao
Answer: 30 cm²

Question 4

M1 8.4*5 oe
A1 42 cm² cao
Answer: 42 cm²

Question 5

(a) B1 p = 6 m (10-4)
(a) B1 q = 3 m (7-4)
(a) Answer: p = 6 m, q = 3 m
(b) M1 10+4+6+3+4+7 oe, ft from part (a)
(b) A1 34 m cao ft
(b) Answer: 34 m
(c) M1 splits shape into two rectangles, or uses bounding rectangle minus notch, method shown
(c) A1 correct sub-areas found, e.g. 28 and 24 (or 70 and 18), ft from part (a)
(c) A1 52 m² cao ft
(c) Answer: 52 m²

Question 6

M1 0.5*(7+11)*4 oe
A1 36 m² cao
Answer: 36 m²

Question 7

(a) M1 2*π*6 oe
(a) A1 awrt 37.7 m
(a) Answer: 37.7 m (3 sf)
(b) M1 π*15 oe
(b) A1 awrt 47.1 cm
(b) Answer: 47.1 cm (3 sf)

Question 8

(a) M1 π*4.5² oe
(a) A1 awrt 63.6 cm²
(a) Answer: 63.6 cm² (3 sf)
(b) M1 0.8*1.2 (=0.96) oe
(b) M1 0.5*π*0.4² (=0.251...) oe
(b) A1 awrt 1.21 m² cao
(b) Answer: 1.21 m² (3 sf)

Question 9

(a) M1 1 m² = 10000 cm² used oe
(a) A1 32000 cm² cao
(a) Answer: 32000 cm²
(b) M1 1 cm² = 100 mm² used oe
(b) A1 2.5 cm² cao
(b) Answer: 2.5 cm²

Question 10

M1 8*5*3 oe
A1 120 cm³ cao
Answer: 120 cm³

Question 11

M1 0.5*5*4 (=10, cross-sectional area) oe
M1 10*9 oe
A1 90 cm³ cao
Answer: 90 cm³

Question 12

M1 three face areas found: 6*4=24, 6*3=18, 4*3=12
A1 sum = 54 oe
A1 108 cm² cao (54 doubled)
Answer: 108 cm²

Question 13

M1 4.2*3.5 (=14.7, area of room) oe
M1 14.7*18.50 oe
A1 GBP 271.95 cao
Answer: 271.95 pounds

Question 14

M1 identifies area 52 m² as the cross-section (ft from Q5)
M1 52*0.1 oe
A1 5.2 m³ cao ft
Answer: 5.2 m³

Question 15

M1 50*30*25 (=37500 cm³) oe
M1 1000 cm³ = 1 litre used
A1 37.5 litres cao
Answer: 37.5 litres

Question 16

(a) M1 (90/360)*2*π*3.5 oe
(a) A1 awrt 5.50 m
(a) Answer: 5.50 m (3 sf)
(b) M1 (90/360)*π*3.5² oe
(b) A1 awrt 9.62 m²
(b) Answer: 9.62 m² (3 sf)

Question 17

(a) M1 4.5*2.6 - (1.2*1) - (0.9*2) oe, complete method
(a) A1 8.7 m² cao
(a) Answer: 8.7 m²
(b) M1 8.7/12 (=0.725 litres needed), ft from part (a)
(b) A1 1 tin cao ft, with reason that 0.725 < 2.5
(b) Answer: 1 tin

Question 18

M1 0.5*3*4 (=6, triangle area) oe
M1 6*2 (=12, two triangular faces) oe
M1 (3+4+5)*12 (=144, three rectangular faces) oe
A1 156 cm² cao (12+144)
Answer: 156 cm²

Question 19

M1 trial e.g. x=3.8 giving 3.8²*6.8=98.19... (too small)
M1 trial e.g. x=3.9 giving 3.9²*6.9=104.95... (too big), narrowing between 3.8 and 3.9
A1 x=3.8 cao (1 dp), supported by checking midpoint 3.85 giving 101.53... (too big, confirms root nearer 3.8)
Answer: x = 3.8 (1 dp)

Question 20

(a) M1 radius = 0.3 m used (diameter converted and halved)
(a) M1 π*0.3²*1.2 oe
(a) A1 awrt 0.339 m³
(a) Answer: 0.339 m³ (3 sf)
(b) M1 1 m³ = 1000 litres used, ft from (a)
(b) A1 awrt 339 litres cao ft
(b) Answer: 339 litres (3 sf)

Geometry: Area, Perimeter and Volume - Worksheets, Questions and Revision

KS3.M-G2 Geometry: Area, Perimeter and Volume

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