Question

Find the surface area of a sphere of radius r, using calculus.

Answer 1

omg i know this

Answer 2

give me just a sec

Answer 3

that would be amazing if you could help! :)

Answer 4

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

Answer 5

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

Answer 6

ok. thanks

Answer 7

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.

Answer 8

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

Answer 9

what is the circumference of sphere

Answer 10

Thanks QuantumModulus, that helped a lot!!

Answer 11

Glad to help. :)

Answer 12

have you done trig substition yet?

Answer 13

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

Answer 14

nvm it is a simple integration

Answer 15

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

Answer 16

let me know what you get?

Answer 17

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

Answer 18

Yes! :)

Answer 19

ignore the extra stuff on that attachment

Answer 20

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