Volume: from the cuboid to the sphere

PYQ (2016-2024 papers)

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Free questions

1. Question 1

   Consider the following statements on packing boxes in a carton. 1. Large volume ÷ small volume is the upper limit on the number of boxes that can be packed. 2. If the three sides of the carton are divisible by the three sides of the box in some order, each by a different side, that number is packed exactly. 3. In the 1 m × 88 cm × 63 cm carton, one of 22, 18 and 10 cm divides 63 cm exactly. Which of these are correct?

   1. A. 1 only
   2. B. 1 and 2 only
   3. C. 2 and 3 only
   4. D. 1, 2 and 3
   Answer and explanation

   ✓ Correct answer: B. 1 and 2 only

   The quotient of the volumes is an upper limit; if the sides divide one to one, that number is packed exactly; but none of 22, 18 and 10 divides 63 (63 = 22 × 2 + 19 = 18 × 3 + 9 = 10 × 6 + 3); so 1 and 2 are correct and 3 is wrong.

   Source: கணக்கு, ஒன்பதாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard IX, Tamil medium; Samacheer Kalvi) (இயல் 7 அளவியல் (7.5 கனச்செவ்வகம், கனச்சதுரத்தின் கனஅளவு), p. 275 (PDF p. 281))

2. Question 2

   How many edges does a cube have?

   1. A. 6
   2. B. 8
   3. C. 24
   4. D. 12
   Answer and explanation

   ✓ Correct answer: D. 12

   A cube has 6 faces, 12 edges and 8 vertices.

   Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 2 அளவைகள் (2.4 முப்பரிமாண வடிவங்கள்), p. 69 (PDF p. 75))