The diagram shows a container in the shape of a cone with a cylinder on top.

The height of the cylinder is 3 times its base radius, r.

The volume of the container must be 5500 cm³.

The base of the cone has a radius of r cm. 

a. Write down an expression for the height of the cone in terms of r.

b. Show that 2πr³ +11πr² - 5500 = 0.

c. The equation in part b has a root, α.

Show that α is also a root of the equation

d. Using an iterative formula based on the equation in part c, and a starting value of 8, find the value of α correct to 3 decimal places. Give the value of each of your iterations to an appropriate degree of accuracy.

e. Explain what information is given by your answer to part d, in the context of the question.

Transcribed Image Text:

3r 33 cm