Question

Find the surface area of the surface S. S is the cap cut from the sphere $x^2 + y^2 + z^2 = 16$ by the cone $z = 8\sqrt{x^2 + y^2}$. $16\left(1 - \frac{8\sqrt{65}}{65}\right)\pi$ $16\left(1 - \frac{8\sqrt{65}}{65}\right)$ $32\left(1 - \frac{8\sqrt{65}}{65}\right)\pi$ $16\left(\frac{8\sqrt{65}}{65} - 1\right)\pi$

          Find the surface area of the surface S.
S is the cap cut from the sphere $x^2 + y^2 + z^2 = 16$ by the cone $z = 8\sqrt{x^2 + y^2}$.
$16\left(1 - \frac{8\sqrt{65}}{65}\right)\pi$
$16\left(1 - \frac{8\sqrt{65}}{65}\right)$
$32\left(1 - \frac{8\sqrt{65}}{65}\right)\pi$
$16\left(\frac{8\sqrt{65}}{65} - 1\right)\pi$

Find the surface area of the surface S.
S is the cap cut from the sphere x^2 + y^2 + z^2 = 16 by the cone z = 8√(x^2 + y^2).
16(1 - (8√(65))/(65))π
16(1 - (8√(65))/(65))
32(1 - (8√(65))/(65))π
16((8√(65))/(65) - 1)π

Added by Suzanne M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Gaurav Kalra

Step 1

The equation of the sphere is x^2 + y^2 + z^2 = 16. The equation of the cone is z = 8√(12^2 + 7^2) - 8√16 = 8√(144 + 49) - 8√16 = 8√193 - 8. To find the equation of the cap surface S, we need to find the intersection points of the sphere and the cone. We can Show more…

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