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)
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)
3
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)
4
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)
5
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)
6
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)
7
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)
8
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)
9
Unit conversions.
(a)Convert 3.2 m2 to cm2.(2)
(b)A small tile has an area of 250 mm2. Convert this to cm2.(2)
10
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)
11
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)
12
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)
13
A rectangular room measures 4.2 m by 3.5 m. New carpet costs 18.50 pounds per m2. Calculate the total cost of carpeting the room.
(3)
14
The L-shaped garden from Question 5 has an area of 52 m2. It is covered with a uniform layer of gravel 0.1 m deep. Calculate the volume of gravel needed.
(3)
15
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)
16
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)
17
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 m2. 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)
18
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)
19
A cuboid has a square base of side x cm and height (x+3) cm. Its volume is 100 cm3. By trial and improvement, find the value of x correct to 1 decimal place. Show at least two trials.
(3)
20
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)