Level 3 Differentiation Walkthrough

2024 NCEA Level 3 Differentiation Question 3(d)

2024 Paper

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Question

Jamie is doing some baking and pouring the flour to form a conical pile.

The height of the pile is always the same as the diameter of the base of the cone.

If the flour is being added at a constant rate of \(3\text{ cm}^3\) per second, at what rate is the height increasing when the pile is \(4\) cm in height?

Note that the volume of a cone is \(V=\frac{1}{3}\pi r^2h\).

You must use calculus and show any derivatives that you need to find when solving this problem.

First walkthrough idea

Hint to try first

The height equals the diameter, so start by linking \(r\) and \(h\).

Step 1

Relate the radius and the height

That substitution is the key step that makes the related-rates algebra manageable.

Show the first step’s working

That substitution is the key step that makes the related-rates algebra manageable.

Key result

\[ r=\frac{h}{2} \]

Walkthrough overview

What this question practises

This 2024 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Related rates for the height of a conical pile.

This is Question 3(d) from the 2024 NCEA Level 3 Differentiation paper for AS91578 — Apply differentiation methods in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91578.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise related rates for the height of a conical pile. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Differentiate with respect to time consistently, then include the correct units and contextual interpretation.

Continue practising

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