Mensuration (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on mensuration and visualising solid shapes for Class 8, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on mensuration and visualising solid shapes at Class 8 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Take π = {22/7} unless stated otherwise. Figures are not drawn to scale.

Sample questions from this worksheet

A preview of what's inside Mensuration (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The area of a trapezium whose parallel sides are a and b and whose height is h is _______.

   • A{1/2}abh
   • B(a + b)h
   • C{1/2}(a + b)hcorrect
   • Da × b × h
   Solution: A trapezium is half of a parallelogram of base (a + b) and height h, so its area is {1/2}(a + b)h — half the sum of the parallel sides, times the distance between them.

2. 2. A cuboidal box measures 10 cm by 8 cm by 6 cm. Its volume is _______.

   • A144 cm³
   • B376 cm³
   • C240 cm³
   • D480 cm³correct
   Solution: Volume of a cuboid = length × breadth × height
   = 10 × 8 × 6 = 480 cm³. (Its surface area would be 2(80 + 48 + 60) = 376 cm², which is offered as one of the distractors.)

3. 3. Consider the following statements.(i) If the side of a cube is doubled, its volume becomes 8 times as large.(ii) A cylinder is a polyhedron.(iii) Two solids with the same volume must have the same surface area.Which of the statements is/are correct?

   • A(i) onlycorrect
   • B(i) and (ii) only
   • C(ii) and (iii) only
   • DAll three
   Solution: Statement (i) is true — volume = s³, so doubling s multiplies the volume by 2³ = 8. Statement (ii) is false; a polyhedron must be bounded entirely by flat polygonal faces, and a cylinder has a curved surface. Statement (iii) is false; a 1 × 1 × 8 cuboid and a 2 × 2 × 2 cube both have volume 8 but surface areas 34 and 24. Hence (i) only.