A storage capsule consists of a right circular cylinder capped by a hemispherical top…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A storage capsule consists of a right circular cylinder capped by a hemispherical top of the same radius rr. The interior volume must be 1800 cm31800\text{ cm}^3. Only the curved surface of the hemisphere and the lateral surface of the cylinder receive an exterior coating; the flat circular base is left uncoated. Which radius rr minimizes the amount of coating required? (a) r=(3600π)1/3 cmr=\bigl(\tfrac{3600}{\pi}\bigr)^{1/3}\text{ cm} (b) r=(1350π)1/3 cmr=\bigl(\tfrac{1350}{\pi}\bigr)^{1/3}\text{ cm} (c) r=(2700π)1/3 cmr=\bigl(\tfrac{2700}{\pi}\bigr)^{1/3}\text{ cm} (d) r=(1800π)1/3 cmr=\bigl(\tfrac{1800}{\pi}\bigr)^{1/3}\text{ cm}

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