Question 487606
Assume the radius of the cylinder is r. Upon drawing the sphere and cylinder, draw a right triangle (with a vertex at the center of the sphere) with legs r and h/2, and hypotenuse 10 (since the distance from the center to the edge of the sphere is 10). This will satisfy the Pythagorean theorem


*[tex \LARGE r^2 + (\frac{h}{2})^2 = 10^2]


*[tex \LARGE r^2 = 100 - \frac{h^2}{4}]


*[tex \LARGE r = \sqrt{100 - \frac{h^2}{4}}]


Now use the volume and surface area formulas:


*[tex \LARGE V = \pi r^2 h]


*[tex \LARGE A = 2\pi r^2 + 2\pi r h]


and replace your expression for r into each of these.