the pretty perfume company designed a new perfume bottle. The bottle is to be a spherical shape with a diameter of 7cm.

Question

a) determine the volume and surface area of this bottle.

b) The spherical bottle has a conical shaped lid with a diameter of 5cm and a height of 4.5cm. Calculate the volume and surface area of the lid. Before you can use the surface area formula for a cone you will need to find the slant height of the lid.

Please show your work so I can understand how to do it.

Answer 1

a) diameter = 2r

Volume = 4/3πr^3

Surface area = 4πr^2

b) Surface area = πr^2 (base) + πrs (cone), where s is diagonal measure of side

Pythagorean theorem, h^2 + r^2 = s^2, to find value of s.

V = 1/3πr^2h

Insert the appropriate values into these formulas.