Lengths in a solid shape are measured in centimetres (cm). What is the correct unit for the volume of the shape?
A) cm
B) cm2
C) cm3
D) cm4
(Total for Question 1 is 1 mark)
2
Which formula correctly gives the volume of any prism?
A) perimeter of cross-section x length
B) area of cross-section x length
C) area of cross-section + length
D) area of cross-section x perimeter
(Total for Question 2 is 1 mark)
3
A cuboid has length 8 cm, width 5 cm and height 3 cm. Diagram: cuboid labelled length 8 cm, width 5 cm and height 3 cm. Work out the volume of the cuboid.
Diagram NOT accurately drawn
(Total for Question 3 is 2 marks)
4
A cube has an edge length of 6 cm. Diagram: cube with every edge labelled 6 cm. Work out the volume of the cube.
Diagram NOT accurately drawn
(Total for Question 4 is 2 marks)
5
A prism has a cross-section that is a right-angled triangle with base 6 cm and height 4 cm. The length of the prism is 10 cm. Diagram: triangular prism, right-angled triangle cross-section with base 6 cm and height 4 cm, prism length 10 cm. Work out the volume of the prism.
Diagram NOT accurately drawn
(Total for Question 5 is 3 marks)
6
A cuboid has a volume of 240 cm3. The length of the cuboid is 8 cm and the width is 5 cm. Work out the height of the cuboid.
(Total for Question 6 is 3 marks)
7
The cross-section of a prism is a trapezium with parallel sides of length 5 cm and 9 cm. The perpendicular distance between the parallel sides is 4 cm. The prism is 12 cm long. Diagram: trapezium cross-section with parallel sides 5 cm and 9 cm and perpendicular height 4 cm between them; prism length 12 cm. Work out the volume of the prism.
Diagram NOT accurately drawn
(Total for Question 7 is 3 marks)
8
The cross-section of a prism is an L-shape. The L-shape is made from a rectangle measuring 10 cm by 8 cm with a smaller rectangle measuring 4 cm by 3 cm cut from one corner. The prism is 5 cm long. Diagram: L-shaped cross-section, large rectangle 10 cm by 8 cm with a 4 cm by 3 cm rectangle removed from one corner; prism length 5 cm. Work out the volume of the prism.
Diagram NOT accurately drawn
(Total for Question 8 is 4 marks)
9
A fish tank is a cuboid with internal dimensions 40 cm by 25 cm by 20 cm. Work out the volume of the tank. Give your answer in litres. (1 litre = 1000 cm3)
(Total for Question 9 is 4 marks)
10
A water tank is a cuboid measuring 50 cm by 40 cm by 30 cm. Water flows into the empty tank at a constant rate of 2 litres per minute. Work out how long it will take to completely fill the tank. Give your answer in minutes.
(Total for Question 10 is 4 marks)
11
Two water containers are both cuboids. Container A measures 12 cm by 8 cm by 5 cm. Container B measures 10 cm by 9 cm by 6 cm. By calculating the volume of each container, determine which container has the greater capacity. You must show your working.
(Total for Question 11 is 3 marks)
12
The cross-section of a prism is a right-angled triangle. The hypotenuse of the triangle is 13 cm and one of the other two sides is 5 cm. The prism is 9 cm long. Diagram: right-angled triangle cross-section, hypotenuse 13 cm, one shorter side 5 cm, third side unmarked; prism length 9 cm. Work out the volume of the prism.
Diagram NOT accurately drawn
(Total for Question 12 is 5 marks)
13
The diagram shows the end of a garden shed. The end is a pentagon made from a rectangle 8 m wide and 5 m tall, with an isosceles triangle on top of the rectangle. The triangle has a base of 8 m and a height of 3 m. The shed is a prism of length 6 m. Diagram: pentagon cross-section formed from a rectangle 8 m by 5 m with an isosceles triangle (base 8 m, height 3 m) on top; prism length 6 m. Work out the volume of the shed.
Diagram NOT accurately drawn
(Total for Question 13 is 5 marks)
14
A builder's skip is in the shape of an open cuboid with length 3 m, width 1.8 m and height 1.2 m.
(a)Work out the volume of the skip in m3.(2)
(b)Given that 1 m3 = 1000 litres, work out the capacity of the skip in litres.(2)
(Total for Question 14 is 4 marks)
15
A cuboid has a square cross-section with side length x cm. The cuboid is 15 cm long. The volume of the cuboid is 540 cm3.
(a)Show that x2 = 36.(2)
(b)Work out the value of x.(2)
(Total for Question 15 is 4 marks)
16
A cylinder has a radius of 4 cm and a height of 10 cm. Diagram: cylinder with radius 4 cm and height 10 cm. Using V = π x r2 x h, work out the volume of the cylinder. Give your answer correct to 3 significant figures.
Diagram NOT accurately drawn
(Total for Question 16 is 3 marks)
17
A prism has a cross-section that is a right-angled triangle. The base of the triangle is x cm and the height of the triangle is (x + 4) cm. The prism is 10 cm long. The volume of the prism is 300 cm3.
(a)Show that x2 + 4x - 60 = 0.(2)
(b)Hence work out the value of x, given that x > 0.(3)
(Total for Question 17 is 5 marks)
18
A garden storage shed is modelled as a triangular prism roof on top of a cuboid. The cuboid part has length 6 m, width 4 m and height 2.5 m. The triangular prism roof has the same length as the cuboid (6 m). The triangular cross-section of the roof has a base of 4 m and a height of 1.5 m. Diagram: cuboid (6 m by 4 m by 2.5 m) with a triangular prism roof on top (triangle base 4 m, height 1.5 m, length 6 m). Work out the total volume of the shed.
Diagram NOT accurately drawn
(Total for Question 18 is 5 marks)
Mark scheme · 4.13 Volume of a Prism
Question 1
B1 cm3 identified (C) cao
Answer: C) cm3
Question 2
B1 B selected cao
Answer: B
Question 3
M1 8 x 5 x 3 oe
A1 120 cao (units cm3)
Answer: 120 cm3
Question 4
M1 6 x 6 x 6 oe
A1 216 cao (units cm3)
Answer: 216 cm3
Question 5
M1 area of triangle = 0.5 x 6 x 4 (= 12) oe
M1 volume = 12 x 10 ft (their area x 10)
A1 120 cao (units cm3)
Answer: 120 cm3
Question 6
M1 8 x 5 (= 40) oe
M1 240 / 40 ft (240 divided by their 40)
A1 6 cao (units cm)
Answer: 6 cm
Question 7
M1 0.5 x (5 + 9) x 4 (= 28) oe
M1 28 x 12 ft (their area x 12)
A1 336 cao (units cm3)
Answer: 336 cm3
Question 8
M1 10 x 8 (= 80) oe
M1 4 x 3 (= 12) oe
M1 (80 - 12) x 5 ft (= 340)
A1 340 cao (units cm3)
Answer: 340 cm3
Question 9
M1 40 x 25 x 20 oe
A1 20000 cao (units cm3)
M1 20000 / 1000 ft (their volume divided by 1000)
A1 20 litres cao
Answer: 20 litres (20000 cm3)
Question 10
M1 50 x 40 x 30 (= 60000) oe
A1 60 litres ft (60000 cm3 converted using 1 litre = 1000 cm3)
M1 60 / 2 ft (their capacity in litres divided by 2)
A1 30 minutes cao
Answer: 30 minutes
Question 11
M1 12 x 8 x 5 (= 480) oe
M1 10 x 9 x 6 (= 540) oe
A1 Container B, with both volumes correctly compared oe
Answer: Container B (540 cm3 compared with 480 cm3)
Question 12
M1 132 - 52 oe (= 144)
A1 12 cao (third side of triangle)
M1 0.5 x 5 x 12 ft (= 30)
M1 30 x 9 ft (their area x 9)
A1 270 cao (units cm3)
Answer: 270 cm3
Question 13
M1 8 x 5 (= 40) oe
M1 0.5 x 8 x 3 (= 12) oe
M1 40 + 12 ft (= 52, total cross-sectional area)
M1 52 x 6 ft (their area x 6)
A1 312 cao (units m3)
Answer: 312 m3
Question 14
(a) M1 3 x 1.8 x 1.2 oe
(a) A1 6.48 cao (units m3)
(a) Answer: 6.48 m3
(b) M1 their (a) x 1000 ft
(b) A1 6480 cao (units litres)
(b) Answer: 6480 litres
Question 15
(a) M1 x2 x 15 = 540 oe
(a) A1 x2 = 540 / 15 = 36 cso (correct working shown leading to the given answer)
(a) Answer: x2 = 36 (shown)
(b) M1√36 ft (their part (a))
(b) A1 x = 6 cao (units cm, positive root only)
(b) Answer: x = 6 cm
Question 16
M1 π x 42 x 10 oe
A1 awrt 502 to 502.7 seen (more accurate unrounded value)