Model and solve related rates problems as instances of the chain rule including situations that involve surface area and volume of cones, pyramids and spheres, with and without technology.

A spherical balloon is being inflated so that its volume is increasing at a constant rate of 100 cm³/s. Calculate the rate at which the radius is increasing, in cm/s, at the instant when the radius is 5 cm. Give your answer correct to two decimal places.

Sand is being poured into a conical container at a constant rate of (0.5 \text{ m}^3\text{/min}\u0005). The container has a fixed apex angle such that the radius of the sand's surface is always equal to the height of the sand. When the sand is 1.2 m deep, find the rate at which the height of the sand is increasing. Give your answer to 2 decimal places.

A conical water tank has a base radius of 3 m and a vertical height of 8 m. Water is being pumped into the tank at a constant rate of 2 m³/min. Determine the rate at which the water level is rising when the depth of water in the tank is 5 m. Note: the radius and height of the water surface maintain the same ratio as the tank dimensions throughout.