An industrial conical mold is being manufactured with a fixed vertical height of 12 cm12\text{ cm}12 cm. The mold has a base radius of r cmr\text{ cm}r cm and a slant height of l cml\text{ cm}l cm.
Determine an expression for l in terms of rl\text{ in terms of }rl in terms of r.
During a specific expansion process, the radius of the base is increasing at a constant rate of 1.5 cm per second1.5\text{ cm per second}1.5 cm per second.
Calculate the rate at which the total surface area of the mold is changing at the instant when the radius is 5 cm5\text{ cm}5 cm. Give your answer in cm2 per second\text{cm}^2\text{ per second}cm2 per second correct to one decimal place.
[The total surface area, SSS, of a cone is given by the formula S=πr2+πrlS = \pi r^2 + \pi rlS=πr2+πrl]
