Question 55
2\. A right circular cylinder has its base area, lateral area and total surface area, in that order, in arithmetic progression.
a) If $v$ is its height, express its radius $r$ in terms of $v$.
b) Suppose its height is $3\,\mathrm m$. How long would it take to fill the cylinder halfway with water flowing in at $0.5$ litre per second? Express the time in hours, minutes and seconds.
Supplemental coordinate illustration (AI); perspective is not to scale.
a) If $v$ is its height, express its radius $r$ in terms of $v$.
b) Suppose its height is $3\,\mathrm m$. How long would it take to fill the cylinder halfway with water flowing in at $0.5$ litre per second? Express the time in hours, minutes and seconds.
Supplemental coordinate illustration (AI); perspective is not to scale.