Sand is poured onto a horizontal surface to form a right circular conical pile. The radius of the ba

Question

Sand is poured onto a horizontal surface to form a right circular conical pile. The radius of the base of the pile is always $\frac{3}{4}$ of its vertical height. The volume of the pile is increasing at a constant rate of $10\text{ cm}^3\text{/s}$. Find the rate at which the curved surface area of the pile is increasing at the instant when its height is $4\text{ cm}$.[5]

Accepted Answer

$\frac{25}{3}\text{ cm}^2\text{/s}$.

Connected Rates for a Conical Sand Pile

Connected Rates for a Conical Sand Pile