A right circular cone with its tip down has a height of and a base radius of

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A right circular cone with its tip down has a height of

15\,\text{m}

and a base radius of

6\,\text{m}

. Water in the cone currently has a depth of

4\,\text{m}

, and the depth is increasing at a rate of

0.03\,\text{m/min}

. Determine the instantaneous rate at which the radius of the circular water surface is changing at that moment. Clearly indicate units and whether the radius is increasing or decreasing.

Related theory

Similarity of Triangles
Similarity
Related Rates
Rates of change
Rate of change of quantities

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