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One brand of tablet is 2 centimeters long and is in the shape of a cylinder with hemispheres of diameter 0.5 centimeter attached to both ends.
A second brand of tablet is to be manufactured in the shape of a right circular cylinder of altitude 0.5 centimeter.
a) Find the diameter of the second tablet so that its surface are is equal to that of the first tablet.
Find the surface area of the 1st tablet
The radius of the two hemispheres = .25
The length of cylinder portion = 2 - .5 = 1.5 cm
S.A = (4*pi*.25^2) + (pi*.5*1.5)
S.A = .7854 + 2.3562
S.A = 3.1416 sq/cm of the 1st tablet
Find the radius of the 2nd tablet (h=.5) with the above S.A.
2*pi*r^2 + 2*pi*r*.5 = 3.1416
Divide both side by 2*pi
r^2 + .5r =
r^2 + .5r = .5
A quadratic equation:
r^2 + .5r - .5 = 0
(r+1)(r-.5) = 0
r = + .5 cm; diameter of the 2nd tablet = 1.0 cm
Check solution: pi*.5^2 + pi*1*.5 = 3.1416 sq/cm
b) Find the volume of each tablet.
Tablet 1; r=.25; h=1.5:
V = (
*pi*.25^3) = (pi*.25^2*1.5)
V = .06545 + .29452
V = .360 cu/cm
Tablet 2; r=.5, h=.5:
V = pi*.5^2*.5
V = .3927 cu/cm