# Science:Math Exam Resources/Courses/MATH110/April 2011/Question 06

MATH110 April 2011
Other MATH110 Exams

### Question 06

Stalagmites are cone-shaped mineral deposits which rise from the floors of limestone caves. They form over millenia as dripping water deposits calcium carbonate onto the cave floor.

Consider a cone-shaped stalagmite with a length always equal to five times its radius. Suppose the stalagmite's height increases at a rate of 0.13 millimetres per year. Write down two expressions for the rate of change of its volume: (i) with respect to its height h, and (ii) with respect to its radius r.

Hint: the volume V of a cone with radius r and height h is equal to ${\displaystyle {\frac {1}{3}}\pi r^{2}h}$.

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