Volume of a prism Quiz (Grade 4)

Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8/9

Topic:

Score: 0 / 10

Volume of a prism — Notes & Worked Examples Show / Hide

Explanation:

A prism is a 3D shape that has the exact same 2D shape (the cross-section) running all the way through its length. For any prism: Volume of Prism = Area of Cross-Section × Length.

Always calculate the area of the front cross-section first (whether it is a triangle, a trapezium, or a compound L-shape), and then multiply that area by the depth/length of the prism.

Example 1: A triangular prism has base 8 cm, perpendicular height 6 cm, and length 12 cm. Find its volume.

Area = 12×8×6 = 24 cm²

V = 24 × 12

= 288 cm³

Example 2: A prism has a trapezium cross-section with parallel sides 5 m and 9 m, height 3 m, and length 10 m. Find its volume.

Area = 5+92×3 = 21 m²

V = 21 × 10

= 210 m³

One Page Guide (PDF) Volume of a prism Worksheets

Question 1

[2 marks]

Calculate the volume of the cylinder
Give your answer to 1 decimal place

cm³

Worked Solution & Answer

(The volume of a cylinder is πr²h) B1

Answer: 785.4 cm³ cm³

Question 2

[2 marks]

Calculate the volume of the triangular prism

m³

Worked Solution & Answer

(The volume of a prism is area of cross-section × length) B1

Answer: 225 m³ m³

Question 3 AQA Nov 2023 2F Q26 / 2H Q7

[3 marks]

Here is a prism drawn on an isometric grid.

Work out the volume of the prism.

Answer cm³

Worked Solution & Answer

(The volume of a prism is area of cross-section × length)
Area of L-shaped cross-section = (2 × 3) + (1 × 1) = 7 cm² M2
Volume = 7 × 6 = 42 cm³. A1

Answer: Answer 42 cm³

Question Paper (PDF) • Mark Scheme (PDF)

Question 4 IGCSE Jan 2020 2HR Q13

[3 marks]

The diagram shows a prism ABCDEFGH in which ABCD is a trapezium with BC parallel to AD and CDEF is a rectangle.

BC = 7 cm AD = 12 cm DE = 10 cm
The height of trapezium ABCD is h cm
The volume of the prism is 608 cm³
Work out the value of h.

h =

Worked Solution & Answer

(The volume of a prism is area of cross-section × length)
0.5 × (7 + 12) × h × 10 = 608 M1
⇒ 95h = 608 M1
⇒ h = 608 ÷ 95 = 6.4 A1

Answer: h = 6.4

Question Paper (PDF) • Mark Scheme (PDF)

Question 5

[3 marks]

The diagram shows a prism placed on a horizontal floor.

The prism has height 4 m
The volume of the prism is 28 m³
The pressure on the floor due to the prism is 65 newtons/m²
Work out the force exerted by the prism on the floor.

newtons

Worked Solution & Answer

(The volume of a prism is area of cross-section × length)
Base area = Volume ÷ height = 28 ÷ 4 = 7 m² M2
Force = pressure × area = 65 × 7 = 455 newtons A1

Answer: 455 newtons

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 Practice Set 5 3F Q9

[3 marks]

The diagram shows a box for chocolates.
The box is in the shape of a triangular prism.

In the space below, draw an accurate net of this box.

Worked Solution & Answer

3 rectangles (3 cm × 4 cm) and 2 equilateral triangles (side 3 cm) M2 A1

Answer: Correct net of triangular prism (three 3 cm × 4 cm rectangles and two 3 cm equilateral triangles) drawn on grid

Question Paper (PDF) • Mark Scheme (PDF)

Question 7 Practice Set 3 1F Q17

[3 marks]

Here is a prism.
It is made by cutting a solid cube of side 2 cm in half.

Find the volume of the prism.

cm³

Worked Solution & Answer

(The volume of a prism is area of cross-section × length)
Volume of cube = 2 × 2 × 2 = 8 cm³ M2
Volume of prism = 8 ÷ 2 = 4 cm³. A1

Answer: 4 cm³ cm³

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 Eduqas Nov 2017 2F Q19

[4 marks]

Work out
(a) Calculate the area of the triangle.
(b) The triangle is the cross-section of the prism shown.
Calculate the volume of the prism.
(c) Another triangular prism has the same cross-section as the one in (b).
The length of the prism is 50 mm.
Without finding the volume of this prism, explain why it has a greater volume than the prism in part (b).

(a) Calculate the area of the triangle. [2 marks]

cm²

(b) The triangle is the cross-section of the prism shown.
Calculate the volume of the prism. [1 mark]

cm³

(c) Another triangular prism has the same cross-section as the one in (b).
The length of the prism is 50 mm.
Without finding the volume of this prism, explain why it has a greater volume than the prism in part (b). [1 mark]

Worked Solution & Answer

(a)

(The area of a triangle is ½ × base × height)
Area = 12 × base × height = 12 × 8 × 5.5 = 22 cm² M1 A1

Answer (a): 22 cm² cm²

(b)

(The volume of a prism is area of cross-section × length)
Volume = Area of cross-section × length = 22 × 4.5 = 99 cm³ B1

Answer (b): 99 cm³ cm³

(c)

(The volume of a prism is area of cross-section × length)
50 mm = 5 cm > 4.5 cm
Since cross-sectional area is identical, volume is directly proportional to length. B1

Answer (c): 50 mm is 5 cm, which is longer than 4.5 cm (longer length with the same cross-section gives greater volume).

Question Paper (PDF) • Mark Scheme (PDF)

Question 9

[5 marks]

The diagram shows a prism.

The cross section of the prism has exactly one line of symmetry.
Work out the volume of the prism.
Give your answer correct to 3 significant figures.

cm³

Worked Solution & Answer

(The volume of a prism is area of cross-section × length)
Roof triangle height h = 5 × tan 40° = 4.1955 cm M2
Area of cross section = (10 × 12) + (0.5 × 10 × 4.1955) = 120 + 20.977 = 140.977 cm² M2
Volume = 140.977 × 25 = 3524.4 cm³ = 3520 cm³ (3 s.f.) A1

Answer: 3520 cm³

Question Paper (PDF) • Mark Scheme (PDF)

Question 10 OCR Jun 2017 2F Q13

[5 marks]

The front and side elevations of a prism, with a pentagon as its cross section, are drawn on this one-centimetre square grid.

(a) Draw accurately the plan of the prism on the grid below. [2 marks]

(b) Calculate the volume of the prism. [3 marks]

cm³

Worked Solution & Answer

(a)

From the front elevation, the prism is 4 cm wide (with a flat top of 1 cm and a sloping roof of horizontal width 3 cm) M1
From the side elevation, the prism is 6 cm long
The plan is a 6 cm by 4 cm rectangle split into a 6 cm by 1 cm strip and a 6 cm by 3 cm strip. A1

Answer (a): 6 cm by 4 cm rectangle drawn with internal line 1 cm from one 6 cm edge

(b)

(The volume of a prism is area of cross-section × length)
Area of pentagonal cross-section (front elevation) = (4 × 1) + (1 × 2) + (12 × 3 × 2) = 4 + 2 + 3 = 9 cm² M1
Length of the prism = 6 cm M1
Volume = cross-sectional area × length = 9 × 6 = 54 cm³. A1

Answer (b): 54 cm³

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 33 marks)

Volume of a prism Worksheets Next: Bearings →

Grade 4 Quizzes

24 Topics

4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction