Reviews
11+ Maths Solved Topic Wise Questions
  • Master weak areas with 10,000+ Questions & Answers
  • Best for 11+ Grammar & Independent School Exams
  • Improve Speed, Accuracy & Time Management
  • Includes 180, Maths Solved Past Papers
1 Year
Full Access
10,000+
Topicwise Questions
180
Solved 11+ Maths Papers

Volume Questions and Answers

Question
Answer
Question 24 - Sevenoaks School Year 7 Entrance Exam 2023

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
2 min
Question
Answer
Question 40 - Merchant Taylors School 11 Plus Maths Specimen Paper 2

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
2 mins
Question
Answer
Question 25 - Merchant Taylors School 11 Plus Maths Specimen Paper 1

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min
Question
Answer

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min 30 sec
Question
Answer
11-plus-maths-Sevenoak-School-2022-Question-12

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min
Question
Answer
Question 13 Sevenoaks School Year 7 Entrance Exam 2021

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
2 min 30 sec
Question
Answer
Question 10 - Kent College Canterbury 11 Plus Entrance Examination 2007

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min 30 sec
Question
Answer

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min
Question
Answer

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
2 min
Question
Answer
Question 26 - The Manchester Grammar School 11 Plus 2005 Arithmetic Paper 2

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min 30 sec
Question
Answer
Question 25 - The Manchester Grammar School 11 Plus 2005 Arithmetic Paper 2

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min
Question
Answer
Question 24 - The Manchester Grammar School 11 Plus 2005 Arithmetic Paper 2

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min
Question
Answer
Question 23 - The Manchester Grammar School 11 Plus 2005 Arithmetic Paper 2

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
45 sec
Question
Answer
Question 22 - The Manchester Grammar School 11 Plus 2005 Arithmetic Paper 2

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min
Question
Answer
Question 17 - The Manchester Grammar School 11 Plus Entrance Examination Arithmetic Paper 2 2007

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
9 min 30 sec
Question
Answer

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
2 min 30 sec
Question
Answer
Question 03 - The Manchester Grammar School 11 Plus Entrance Examination Arithmetic Paper 2 2007

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
2 min 30 sec
Question
Answer
Question 02 - The Manchester Grammar School 11 Plus Entrance Examination Arithmetic Paper 2 2007

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
1 min 30 sec
Question
Answer
Question 32 - The Manchester Grammar School 11 Plus 2005 Arithmetic Paper 1

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
2 min 30 sec
Question
Answer

These detailed answers are visible only for premium members

Please register to unlock over one hundred and sixty 11+ Exam Papers. 10,000+ Questions with Answers

 

Register

 

Login

Solve in:
2 min
1 2 3 4

Volume of 3D Shapes for 11 plus exams

1. What is Volume?

Volume is defined as the amount of space taken up by an object of three dimensions. It is measured in cubic units. Some of the common units of volume are  and cm³. If you take a glass and fill it completely with water, the amount of water present in the glass is the volume of the glass.

All 3D shapes have a volume which can be calculated using the formula specified for that shape. The general idea to workout the volume of any 3D shape is: area of cross section times height.

Let us learn the formulas for the volumes of 3D Shapes covered in 11 plus examinations.

1.1 Cube: Volume formula and solved example

Cube is one of the simplest three-dimensional shapes with all the dimensions of the same size. It has six-square faces, eight vertices, and twelve edges. 

All the six faces of cubes are squares, a two-dimensional face.

For a cube of side a,

01 Volumes

Using the general idea of volume as the area of cross section × height,

For cube, area of cross section = area of square

Volume of cube = Area of square face × height

                           = a² × a

Volume of cube =

Example: A wooden cubic box has a volume of 64 cm³. Work out the side length of the box.

Solution: Let a be the side length of the cubic box.

                Volume of cube =

                 So,  = 64

                      a × a × a = 4 × 4 × 4

                      a = 4  cm

                  The side length of the box is 4 cm

1.2 Cuboid: Volume formula and solved example

A cuboid is a three-dimensional shape with the dimensions as length, width, and height. It has six rectangular faces, eight vertices, and twelve edges.

Let l,w and h be the length, width, and height of the cuboid respectively.

02 Volumes

Using the general idea of volume as the area of cross-section × height,

For the cuboid, area of cross-section = area of rectangle

Volume of cuboid

= Area of rectangle × height

Volume of cuboid = l × w × h

Example: The base of Sarah’s fish tank is 60 cm long and 20 cm wide. If the height of the fish tank is 30 cm, what is the maximum volume of water the tank can hold?

Solution: Maximum volume of water in the tank is the tank’s volume

               The tank is in a cuboid shape.

                Length of tank (l) = 60 cm

                Width of tank (w) = 20 cm

                Height of tank (h) = 30 cm

                Volume of cuboidal fish tank = l × w × h

                                                              = 60 × 20 × 30

                                                              = 36000  cm³

                 Maximum volume of water the tank can hold is 36000  cm³.

2. Volume of Prisms

Prisms are 3D shapes which have the same face on both the ends. It has a constant area of cross-section throughout.

2.1 Finding the volume of a triangular prism.

A triangular prism is a 3D shape consisting of two triangular ends connected by three rectangles.  The triangular ends of a triangular prism are exactly the same.

03 Volumes

We can calculate the volume of this triangular prism by simply multiplying the area of one triangle with the prism's height.

The volume of triangular prism = Area of triangle × height of prism

Example 1: Calculate the volume of the triangular prism shown below.

04 Volumes

Solution: Volume of triangular prism = Area of triangle × height of prism

                 Area of triangle = 1⁄2 × base × height

                                          = 1⁄2× 9 × 5

                                          = 45⁄2

                                          = 22.5 in²

Volume of triangular prism  = 22.5 × 15 = 337.5 in³

Example 2: Work out the volume of the pentagonal prism shown below.

05 Volume

Solution: Volume of pentagonal prism = Area of pentagon × height of prism

               Area of pentagon = 50 mm²                         

                Volume of pentagonal prism  = 50 × 15

                                                           = 750 mm³

Now think about prisms that have rectangular faces at both the ends. Such prisms are called rectangular prisms. Rectangular prisms are nothing but cuboids and so the volume of rectangular prisms is equal to the volume of cuboids.

Quiz Questions
32. Volume
11+ Maths Topicwise Worksheets Banks

Volume worksheet

 

 

 

11 Plus Maths Topic Wise Article
Get This Worksheet
Topicwise Artice Worksheet Form (#43)

11+ Maths Topics

  • Composite Shapes (1)
  • Measurement (331)
  • Time (284)
  • Number Patterns and Sequences (313)
  • Temperature (60)
  • Data Collection and Presentation (7)
  • Networks (10)
  • Shortest time (1)
  • Numbers (3,443)
  • Clock (2)
  • Recipes and Proportions (23)
  • Speed Distance Time (99)
  • Profit and loss (5)
  • Alphabet codes (10)
  • Money (392)
  • Logical Problems (709)
  • Time table (14)
  • Age Problems (42)
  • Permutation and Combinations (99)
  • Probability (97)
  • Patterns and Sequences (92)
  • Scale reading (41)
  • Train Timetables (15)
  • Algebra (970)
  • Statistics (452)
  • Ratio and Proportion (177)
  • Currency Conversions (72)
  • Average (2)
  • Other (8)
  • Geometry (1,121)
  • Magic square (27)
  • Scale Drawings (35)
  • Logical Word Problems (8)
  • Frequently Asked Questions
    What is a good score in 11+ Maths ?

    What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.

    How to prepare for the 11+ Maths exam?

    The best way to prepare for the 11+ Maths Exam is by practicing 11+ Maths topic-wise questions regularly.

    Can I cancel my subscription?

    Maths online subscriptions are “Non-Refundable“. No refunds can be issued for any reason. This is because of the nature of digital products.

    You should, therefore, make sure that the Maths online subscriptions fulfil your needs before you subscribe.

    As these are digital products, we advise parents to go through our Free Past Papers provided on our website and once decided they can buy subscriptions.

    Maths:
    11+ Sample Paper with answers - 1

    11+ Sample Paper with answers - 2

    What kind of questions are asked in the 11 Plus Maths exam?

    The majority of the 11 Plus Maths questions are mathematical problem-solving, where pupils need to understand and apply mathematical concepts. With regular practice of 11+ Maths Topic-wise questions, you will pass the 11-plus Maths Exam with a high score.

    What do you need to know for the 11 Plus Maths exam?

    The children must master the following topics for the 11 plus exams

    • Number and place value.
    • Addition, subtraction, multiplication, and division.
    • Fractions, percentages, decimals.
    • Ratio and proportion.
    • Algebra.
    • Measurement.
    • Geometry (properties and position of shapes, coordinates)
    • Statistics.

    Get 10,000+ Topic-wise questions by subscribing to our 11+ Maths Topic-wise questions. These questions are collected from 180+ Maths past papers.

    What is subscription term ?

    11 Plus Maths Past Papers Subscription

    Any PiAcademy Memberships are for 1 year (366 days), We give Instant unlock to all exam Resources So that you can plan your 11+ Preparation according to your convenience and as per our Planner Spreadsheets.

    Check All Courses >>

    © 2014 - 2024 PiAcademy Limited, All Rights Reserved

    calendar-fullcrossmenu
    >
    linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram