Find the volume of a circular cylinder of height 4 cm whose curved surface area is 176 sq.cm

Question

Find the volume of a circular cylinder.

Answer 1

Volume  of cylinder V = ∏r^2h

h = 4cm, ∏ = 22/7

Surface area of cylinder = 2∏r(r+h)

176 = 2*22/7*r(r+4)

176 = (44/7)r(4+r)

Multiple to each side by 7.

1232 = 44r(4+r)

Multiple to each side by 44.

28 = 4r+r^2

Subtract 28 from each side.

r^2+4r-28 = 0

r = [-4±√(16+112)]/2

r = [-4±√128]/2

r = [-4±11.31]/2

r = [-4+11.31]/2 and r = [-4-11.32]/2

r = 3.65 and r = -7.66

Circle is base of cylinder.

Radius of circle = 3.65 cm

Volume of cylinder v = ∏r^2h

V = 22/7*13.69*4

V = 172.10cm^3