# Analyse the engineering situations and solve engineering problems using calculus

*label*Calculus

*timer*Asked: Jan 4th, 2018

**Question description**

- If the volume of a circular cylindrical block is equal to 750 cm
^{3 }show that the total surface area = 2π x^{2 }+ 1500/x cm^{2}where x cm is the radius of the base. Hence obtain the value of x which makes the surface area a minimum. - Determine the volume of revolution formed by rotating the area enclosed by the curve y = 3/x, the x-axis and the lines x = 1 and x = 2 through 360 degrees about the x-axis. Sketch the volume generated by this revolution

Determine higher order derivatives for algebraic functions in part a)

- The displacement of a particle in simple harmonic motion is given by x = A cos(ωt) + B sin(ωt) where ω represents the angular frequency and A and B are constants. Show that d^2x/dt^2 + ω
^{2}x = 0