Question: The line segment joining the origin to the point (h,r)is revolved aboutthe x-axis to generate a cone of height h and base radius r. Find
The line segment joining the origin to the point (h,r)is revolved aboutthe x-axis to generate a cone of height h and base radius r. Find the cone'ssurface area with the parametric equations x=ht,y=rt,0t1. Check yourresult with the geometry formula: Area =r(slant height).If a smooth curve x=f(t),y=g(t),atb,is traversed exactly once astincreases from atob, then the areas of the surfaces generated by revolvingthe curve about the coordinate axes are as follows.For a revolution about the x-axis (y0) use the formula below.S=ab2y(dxdt)2+(dydt)22dtFor a revolution about the y-axis (x0) use the formula below.S=ab2x(dxdt)2+(dydt)22dtFirst, find the derivative ofx and yin terms oft.dxdt=,dydt=
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
