Maths · Mensuration · chapter 12 of 14

Class 10 Maths Chapter 12: Surface Areas and Volumes Assertion-reason questions with answers

2 assertion-reason questions on Surface Areas and Volumes, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): Two identical cubes joined face to face form a solid whose total surface area is less than the sum of the total surface areas of the two cubes. Reason (R): The two faces at the join are inside the new solid and are no longer part of its surface.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

Both true, and R is exactly why: two faces of area a² each are lost at the join, so TSA = 12a² − 2a² = 10a².

Question 2
Assertion (A): The volume of a solid made of a cone of radius 3 cm and height 4 cm fixed on a hemisphere of radius 3 cm is 30π cm³. Reason (R): The curved surface area of a hemisphere of radius r is 2πr².
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

A: (1/3)π(9)(4) + (2/3)π(27) = 12π + 18π = 30π cm³, true. R is a true formula, but it is about surface area and does not explain a volume.

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