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CUET Mathematics 2026 PYQs30 May Shift 2. Free, no login required.

Calculus

past year questions, CUET Mathematics 2026 30 May Shift 2

Application of Derivatives

past year questions, Calculus, CUET Mathematics 2026 30 May Shift 2

Medium

core

A closed right circular cylinder has a volume of 2156 cm³. The radius of its base so that its total surface area may be minimum, is equal to:

Solution

✅ Correct Option: 1

With V=πr2h=2156V=\pi r^2h=2156, S=2πr2+2πrh=2πr2+2VrS=2\pi r^2+2\pi rh=2\pi r^2+\frac{2V}{r}.

dSdr=4πr−2Vr2=0⇒r3=V2π=2156×72×22=343\frac{dS}{dr}=4\pi r-\frac{2V}{r^2}=0\Rightarrow r^3=\frac{V}{2\pi}=\frac{2156\times7}{2\times22}=343.

So r=7r=7 cm, and S′′>0S''>0 confirms a minimum.

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Match the LIST-I with LIST-II

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