anonymous 5 years ago Find the surface area of a sphere of radius r, using calculus.

1. myininaya

omg i know this

2. myininaya

give me just a sec

3. anonymous

that would be amazing if you could help! :)

4. myininaya

so the equation of a circle having center (0,0) is x^2+y^2+r^2

5. myininaya

oh surface area not volume one sec. let me rething my strategy

6. anonymous

ok. thanks

7. anonymous

Use the formula for the surface area of a general equation revolved around the x-axis. If you start with x^2 + y^2 = r^2, and your function is y, then f(x) = sqrt(r^2-x^2). The formula for the surface area of revolution is, in this case, $SA = 2 \pi* \int\limits_{-r}^{r} \ \ f(x) * \sqrt{1+f(x)^2}$ Integrate and simplify.

8. anonymous

Sorry, inside the root of the integrand it should be f'(x)^2.

9. myininaya

what is the circumference of sphere

10. anonymous

Thanks QuantumModulus, that helped a lot!!

11. anonymous

Glad to help. :)

12. myininaya

have you done trig substition yet?

13. myininaya

I think you may have to do in one of the steps

14. myininaya

nvm it is a simple integration

15. myininaya

16. myininaya

ok but i think was suppose to get 4pi*r^2

17. myininaya

let me know what you get?

18. myininaya

ok it is 4*pi*r^2 because the semicirlce is being revolved about the x axis

19. myininaya

Yes! :)

20. myininaya

ignore the extra stuff on that attachment

21. myininaya

I have to go. You can check your work with the attachment just ignore the But part. goodnight