SOLUTION: A vitamin tablet is 2.4 cm long and is in the shape of a cylinder with hemispheres of diameter 0.6 cm attached to both ends. Another vitamin tablet is in the shape of a cylinder of

Question 818790: A vitamin tablet is 2.4 cm long and is in the shape of a cylinder with hemispheres of diameter 0.6 cm attached to both ends. Another vitamin tablet is in the shape of a cylinder of height 0.6 cm. Find:
a) The radius of the cylindrical tablet given that it's surface area is equal to that of the first tablet, and,
b) The volume of each tablet.
Ans a) 0.6
b)0.622 cm(cube), 0.679 cm(cube)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The 2.4 cm long tablet has an overall length of 2.4 cm (including those two hemispheres at both ends).
It has two hemisphere end caps with radius 0.3 cm attached to the bases of a cylinder with a height of
2.4 cm - 0.3 cm - 0.3 cm = 1.8 cm.
Its surface area is the lateral area of the cylindrical part,
plus the area of the two hemispheres (the area of one sphere).
Its volume is the volume of the cylindrical part,
plus the volume of the two hemispheres (the volume of one sphere).

Formulas:
area of a sphere =
volume of a sphere =
lateral area of a cylinder =
total area of a cylinder =
volume of a cylinder =
where = radius and = height,
which we will measure in cm.

Surface area of the 2.4 cm long tablet (in ):

Surface area of the cylindrical tablet (in ):

If the surface areas are the same,

dividing both sides of the equal sign by we get

Solving by completing the square

is the only useful (positive) solution.
so and -->

Volume of the 2.4 cm long tablet (in ):

Volume of the cylindrical tablet (in ):

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