I'm having some problems getting started on some Calculus problems here. (I know, complete answers aren't supposed to be given out, but I don't even know how to approach the problem [Yes, I've already tried to re-read the notes + textbook, but to no avail]. I missed a week of classes due to being sick so am trying to catch up).
1) "A sector S of a circle with radius R whose angle at the centre of the circle is φ radians, is rolled up to form the curved surface of a right cone standing on a circular base. The semi-vertical angle of this cone is θ radians. Express φ in terms of sin θ and show that the volume V of the cone is given by 3V = πR^3 sin^2 θ cos θ. If R is constant and θ varies, ﬁnd the positive value of tan θ for which dV/dθ = 0. Also, show further that when this value of tan θ is taken, the maximum value of V is obtained. Therefore show that the maximum
value of V is( 2πR^3√3)/27 "
2) A water trough with vertical cross-section in the form of an equilateral triangle is being filled at a rate of 4 cubic metres per minute. Given that the trough is 12 metres long, how fast is the level of the water rising when the water reaches a dept of 1.5 metres."
With no formula to work with, am I supposed to graph it first or something?