Calculus help, please!?

Question

Find the area of the surface obtained by revolving y=25-x^2 around the y axis on the interval [0,5].

Please explain how you'd do it. Thank you!

Answer 1

      (Apply integration)

   (Apply limits)

  (Simplify)

      

Therefore The surface area = 83.33sq.units.

Answer 2

For rotation about y - axis ,the surface area formula is

• The curve equation is

In this case the interval is [0,5], So a = 0 and b = 5.

• Our formula becomes

Substitute the values in integration.

surface obtained by revolving y = 25 - x^2 around the y axis on the interval [0,5] is

 .