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GCSE · Geometry and Measures

4.13 Volume of a Prism

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

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)

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)

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)

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)

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)

A cuboid has a volume of 240 cm^3. 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)

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)

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)

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)

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)

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)

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)

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)

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 m^3.(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)

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 cm^3.

(a)Show that x² = 36.(2)

(b)Work out the value of x.(2)

(Total for Question 15 is 4 marks)

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)

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 cm^3.

(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)

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)
A1 503 cao (3 s.f., units cm³)
Answer: 503 cm³ (3 s.f.)

Question 17

(a) M1 10 x 0.5 x x(x + 4) = 300 oe
(a) A1 x² + 4x - 60 = 0 cso (correct rearrangement shown)
(a) Answer: x² + 4x - 60 = 0 (shown)
(b) M1 (x + 10)(x - 6) = 0 oe (or correct use of the quadratic formula)
(b) A1 x = 6 and x = -10 identified
(b) A1 x = 6 cao (positive root selected since x > 0)
(b) Answer: x = 6 cm

Question 18

M1 6 x 4 x 2.5 (= 60) oe (cuboid volume)
M1 0.5 x 4 x 1.5 (= 3) oe (triangle area)
M1 3 x 6 ft (= 18, roof volume)
M1 60 + 18 ft (total volume)
A1 78 cao (units m³)
Answer: 78 m³

Volume of a Prism - Worksheets, Questions and Revision

4.13 Volume of a Prism

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