Assertion-Reason Questions
Q1: Assertion (A): Two cylinders with equal volume will always have equal surfaces area.
Reason (R): Volume of a cylinder is given by πr²h.
Step 1: Analyze the assertion:
Two cylinders may have the same volume but different dimensions of radius and height.
For example:
Cylinder 1: radius = \(r_1\), height = \(h_1\)
Cylinder 2: radius = \(r_2\), height = \(h_2\)
If \( \pi r_1^2 h_1 = \pi r_2^2 h_2\), volumes are equal.
But surface areas:
\[
SA_1 = 2 \pi r_1 (r_1 + h_1) \\
SA_2 = 2 \pi r_2 (r_2 + h_2)
\]
may be different because \(r\) and \(h\) can vary.
Therefore, Assertion (A) is false.
Step 2: Analyze the reason:
Volume formula for cylinder is correctly stated as:
\[
V = \pi r^2 h
\]
Reason (R) is true.
Answer: d. Assertion (A) is false but Reason (R) is true.
Q2: Assertion (A): Lateral surface area of a cuboid is equal to area of four walls of a room.
Reason (R): Lateral surface area of a cuboid = 2h (l + b).
Step 1: Analyze Assertion (A):
The lateral surface area (LSA) of a cuboid is the sum of the areas of the four vertical walls when considered as a room. So, the assertion is true.
Step 2: Analyze Reason (R):
The formula for lateral surface area of a cuboid is:
\[
LSA = 2h (l + b)
\]
which is the sum of the areas of the four walls.
So, Reason (R) is true.
Step 3: Is Reason (R) the correct explanation of Assertion (A)?
Yes, because the lateral surface area formula directly represents the total area of the four walls of a room.
Answer: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
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