# mathematics

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

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.

• mathematics -

volume of sphere = (4/3)π r^3
surface area = 4π r^2

sub in r = 3.5 into both equations.

b) the surface area of a cone, without its base, is
πrs, where s is the slant height, and r is the radius.
we have to first calculate s by
s^2 = 2.5^2 + 4.5^2
s = √26.5

so surface area = π(2.5)(√26.5))
= ....

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