We are given a right circular cylinder can whose radius r, given in inches, equa

Question

We are given a right circular cylinder can whose radius r, given in inches, equals half its height. Using differentials, by approximately how much does the total surface area of this right circular cylinder can (also include top and bottom) increase when the radius is increased from 5 inches to 5.1 inches? use 3.14 for pi Hint: first state the total surface area S formula for this can.

a) Total surface area S=________ (FORMULA FOR THIS CAN)

b) Approximate Surface area increase; __________ (use differentials)

Explanation / Answer

r=h/2

a)total surface area s=2pir^2 +2pirh =2pir^2 +2pir*(2r) =2pir^2 +4pir^2 =6pir^2

b)dr=5.1-5=0.1

ds=12pir*dr

ds=12*pi*5*(0.1)

ds=18.85 square inches

area increases by 18.85 square inches

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