Specialist2025 NHT Exam 2 Section A · Q7CAS active1 mark

Related rates for water in a leaking cone

Water is poured at a rate of $5 \text{ cm}^3\,\text{s}^{-1}$ into an inverted right circular cone of height $20$ cm and radius $10$ cm, as shown below.

Water flows through a hole at the vertex of the cone at a rate of , where cm is the depth of water in the cone at time seconds, and is an arbitrary positive constant.

The rate at which the depth of water is increasing when the depth of water is $h$ cm is

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\dfrac{5-k\sqrt{h}}{3\pi h^2}

\dfrac{5-k\sqrt{h}}{4\pi h^2}

\dfrac{4\left(5-k\sqrt{h}\right)}{\pi h^2}

\dfrac{5-k\sqrt{h}}{\pi h^3}

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