Question

The volutne or the largest cone that can be inscribed in a sphere of radius 9cm

Answer 1

Answer:

Step-by-step explanation:

The height h is the distance from the apex to the circular base. It is between 0 and 2r (with r the radius of the sphere), and the radius of the base grows as h increases from 0 to r and then shrinks again as h increases to 2r. A diagram may convince you that by Pythagoras (h−r)2+x2=r2, where x is the radius of the base. That allows you to eliminate x2 in favour of 2rh−h2, so you have V(h)=13(2rh−h2)h and thus V′(h)=13(4rh−3h2), which vanishes at h=43r and thus x=8√3r, with maximal volume V=13π89r243r=3281πr3=827Vs, where Vs is the volume of the sphere.