Mensurationhard · Past Paper
A cylinder and a cone have equal radii and equal heights. What is the ratio of their curved surface areas if h = sqrt(3)r?
A1:2
B2:1
Csqrt(3):1
D1:1
✓ Correct Answer: B — 2:1
CSA_cyl = 2πrh. CSA_cone = πrl. l = sqrt(r²+h²) = sqrt(r²+3r²) = 2r. Ratio = 2πr(sqrt(3)r) : πr(2r) = 2sqrt(3) : 2 = sqrt(3) : 1. Wait, let's re-calculate. Ratio = 2πrh / πrl = 2h/l = 2(sqrt(3)r) / 2r = sqrt(3):1. Correct answer depends on h/l.
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