A closed cylindrical tank of a height of 4 meters is to be built so that the total surface area is 10π m2 . Find the radius of the tank.

Answer 1

radius = 1 meter

Surface Area = A = 2pi(r^2) + 2pi(r)h

= the area of the top & bottom plus area of the side

area of top or bottom is pi(r^2)

area of the side is circumference times height = pi times diameter times height or pi x 2r x h

2pi(r^2) + 2pi(r)(4) = 10pi

divide by pi

2r^2 +8r = 10

divide by 2

r^2 + 4r = 5

r^2 + 4r -5 = 0

factor

(r-1)(r+5) =0

r=5 or 1 meter radius

(ignore the negative solution)

r= 1 meter

or you could have completed the square or used the quadratic formula

r^2 +4r = 5, add 4 to both sides

r^2 +4r + 4 = 5 +4 = 9

(r+2)^2 = 9

r+2 = + or - 3

r = 3-2 or -2-3 = -5 or 1

r^2 +4r - 5 = 0

r =-4/2 + or - (1/2)sqr(16+4(5)) = -2 + or - (1/2)6

= -2-3 or -2 +3 = -5 or 1

r = 1

Volume = V = pi(r^2)h = 4pi m^3

V= about 12.57 cubic meters volume