GATE 2024 CH Q47, Mathematics: The correct answer is A, 3πa²/2 | ChemeGate

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GATE 2024 Chemical Engineering, Q47 · Mathematics

The correct answer is A, 3πa²/2.

Question

Let r and $θ$ be the polar coordinates defined by x = r cos $θ$ and y = r sin $θ.$ The area of the cardioid r = a(1 − cos $θ), 0 \leq θ \leq 2π,$ is

Figure for Q47 (Mathematics, Polar Coordinates): Let r and θ be the polar coordinates defined by x = r cos θ and y = r sin θ. The area of the cardioi…

A. $3πa²/2$
B. $2πa²/3$
C. $3πa²$
D. $2πa²$

Official answer: $3πa²/2$

Why

GATE 2024 official key: (A). The area enclosed by the cardioid $r=a(1−cosθ)$ is a standard result: Area $= (1/2)\int ₀^{2π} r² dθ = 3πa²/2.$

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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