Problema Solution
Making a can, A can in the shape of a right circular cylinder is required to have a volume of 250 cubic centimeters.(a)Express the amount A of material to make the can as a function ofthe radius r of the cylinder.
(b) How much material is required if the can is of radius 3 centimeters.?
Answer provided by our tutors
let
r = the radius of the cylinder
h = the eight of the cylinder
V = 250 cm^3 the volume
V = pi*r^2*h
h = V/(pi*r^2)
h = 250/(pi*r^2)
(a) Express the amount A of material to make the can as a function of the radius r of the cylinder.
A = the area of the cylinder or the amount of material to make the can
A = (2*pi*r^2) + (2*pi*r*h)
plug h = 250/(pi*r^2) into the last equation
A = (2*pi*r^2) + (2*pi*r*(250/pi*r^2))
A = (2*pi*r^2) + 550/r
(b) How much material is required if the can is of radius 3 centimeters?
for r = 3 cm
A = (2*pi*3^2) + 550/3
A = 18pi + 550/3
pi = 3.14
A = 18*3.14 + 550/3
A = 239.85 cm^2
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239.85 cm^2 of material is required to make the can.