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 388008: 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.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
formulas that apply:
area of a circle = pi*radius^2
circumference of circle = 2 *pi *radius
area of cylinder = 2 *pi *radius *h
area of sphere or 2 hemispheres= 4*pi*radius^2
volume of a sphere = 4/3 *pi*radius^3
volume of clinder =pi*radius^2*h
pi = 3.14
surface area of first tablet = surface area of cylinder + surface are of 2 hemispheres on each end
surface area of cylinder = (2 *pi *radius *h) =2*pi*.3*2.4=4.52
surface area of 2 hemispheres =4*pi*radius^2 = 4*pi*.3^2=1.13
surface area of first tablet = 4.52+1.13 = 5.65 cm^2
a)as stated, area of second tablet =area of first tablet =2 *pi *radius *.6=5.65
radius = 5.65/(2*pi*.6) = 1.5 cm
b) volume of first tablet = (4/3 *pi*radius^3)+(2 *pi *radius^2 *h)
=(4/3 *pi*.3^3)+(2*pi*.3^2*2.4)=.113+1.36 =1.47 cm^3
volume of second tablet = pi*radius^2*h=pi*1.5^2*.6 =4.24 cm^3

ans: a) The radius of the second tablet is 1.5 cm
b) The volume of the first tablet is 1.47 cm^3
The volume of the second tablet is 4.24 cm^3
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