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put this solution on YOUR website! 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
Factors to:
(r+1)(r-.5) = 0
Positive solution
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
