You work for a perfume company and are being asked to design two new perfume bottles to go with a line of perfume for teen girls. The bottle they have now is a cylinder and has a base radius of 2 cm and a height of 9 cm. They want each of the new bottles to hold the same about of perfume as the original but for them to each be a different shape. One should be a cone, and one a sphere.

You are in charge of designing the bottles, what dimensions would you choose for the sphere and cone shaped bottles? Explain how you know that each bottle would hold the same amount of liquid as the original bottle.