Pre calculus 12 grade

Question

A right circular cylinder with height h and base raduis r has a total surface area of 90 pi square inches .

Express the volume of the cylinder as a function of r

Answer 1

V = 45r - pir^3 = r(45 - pir^2)

Total Surface Area = SA = 90pi in^2 = top&bottom area + side area = 2 times pir^2 + pidh

= 2pir^2 + 2pirh

= 2pir(r+ h) = 90pi

2r(r+h) = 90

2r^2 + 2rh = 90

r^2 + rh = 45

h = (45 - r^2)/r = 45/r - r

V = hpir^2 = (45/r- r)pir^2

V = 45pir -pir^3

Answer 2

Area, A= 2πrh+2πr² = 90

h = (90-2πr²)/(2πr) = (45-πr²)/(πr)

Volume, V= πr²h

V(r) = πr²(45-πr²)/(πr) = r(45r-πr²) = 45r-πr³