Mensuration Statistics and Probability (Class 9)

What this worksheet covers

This is an eighteen-question practice worksheet on mensuration, statistics and probability for Class 9, 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, statistics and probability at Class 9 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. 4Take π = 22/7 wherever it is needed. There is no negative marking.
5. 5Figures are not drawn to scale unless stated. Rough work may be done at the side of each page.

Sample questions from this worksheet

A preview of what's inside Mensuration Statistics and Probability (Class 9) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. By Heron’s formula, the area of a triangle with sides a, b, c and semi-perimeter s is _______.

   • A√(s(s − a)(s − b)(s − c))correct
   • Bs(s − a)(s − b)(s − c)
   • C√(s(a + b + c))
   • D{1/2}(a + b + c)
   Solution: Heron’s formula gives the area purely from the three sides as √(s(s − a)(s − b)(s − c)), where s = {a + b + c/2}. The last option is the semi-perimeter itself, not an area.

2. 2. A cylindrical water drum has base radius 7 cm and height 10 cm. Its volume is _______.

   • A440 cm³
   • B2200 cm³
   • C770 cm³
   • D1540 cm³correct
   Solution: Volume = πr²h = {22/7} × 7 × 7 × 10. One 7 cancels the denominator, leaving 22 × 7 × 10 = 1540 cm³.

3. 3. An isosceles triangle has a perimeter of 32 cm and each of its two equal sides measures 10 cm. Its area is _______.

   • A48 cm²correct
   • B36 cm²
   • C60 cm²
   • D96 cm²
   Solution: The base is 32 − (10 + 10) = 12 cm, so s = 32 ÷ 2 = 16 cm. By Heron’s formula the area is √(16 × 6 × 6 × 4) = √2304 = 48 cm². Checking with the altitude: half the base is 6 cm, so the height is √(100 − 36) = 8 cm and {1/2} × 12 × 8 = 48 cm².