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

Algebra ->  Surface-area -> 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      Log On


   

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) About Me  (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 = 4pi%2Ar%5E2
volume of a sphere = 4pi%2Ar%5E2
lateral area of a cylinder = 2pi%2Ar%2Ah
total area of a cylinder = 2pi%2Ar%5E2%2B2pi%2Ar%2Ah
volume of a cylinder = pi%2Ar%5E2%2Ah
where r= radius and h= height,
which we will measure in cm.

Surface area of the 2.4 cm long tablet (in cm%5E2 ):
2pi%2A0.3%2A1.8%2B4pi%2A0.3%5E2=1.08pi%2B0.36pi=1.44pi
Surface area of the cylindrical tablet (in cm%5E2 ):
2pi%2Ar%5E2%2B2pi%2Ar%2A0.6=2pi%2Ar%5E2%2B1.2pi
If the surface areas are the same,
2pi%2Ar%5E2%2B1.2pi=1.44pi
dividing both sides of the equal sign by pi we get
2r%5E2%2B1.2=1.44
dividing both sides of the equal sign by 2 we get
r%5E2%2B0.6=0.72
Solving by completing the square
r%5E2%2B0.6%2B0.09=0.72%2B0.09
%28r%2B0.3%29%5E2=0.81
r%2B0.3=sqrt%280.81%29 is the only useful (positive) solution.
so r%2B0.3=0.9 and r=0.9-0.3 --> highlight%28r=0.6cm%29

Volume of the 2.4 cm long tablet (in cm%5E3 ):
pi%2A0.3%5E2%2A1.8%2B4pi%2A0.3%5E3%2F3=0.162pi%2B0.036pi=1.98pi%22=+about%22highlight%280.622cm%5E3%29
Volume of the cylindrical tablet (in cm%5E3 ):
pi%2A0.6%5E2%2A0.6=0.216pi%22=+about%22highlight%280.679cm%5E3%29