1

Find the largest possible volume of a cylinder inscribed in a cone with a height of 8 cm and radius of 4 cm.

Do I use the equation for the volume of a cylinder or cone?

Amanda
  • 31
  • 1
    You need to maximize the volume of the cylinder, so use the equation for the volume of a cylinder. The trick is going to be that the height of the cylinder and its radius will be related because it is inscribed inside of a cone. – Mike Pierce Nov 11 '14 at 23:05

1 Answers1

1

You are trying to find the volume of a cylinder. Thus, you should use the formula for the volume of a cylinder.

Think about the different cylinders that can fit inside a cone. The cylinder can be short and wide, or tall and narrow. For a given height there is a maximum radius that can fit inside the cone. Find a formula for the volume of the inscribed cylinder in terms of its height, and use some calculus to find the maximum of this function.

augurar
  • 1,856