A cylinder whose base radius is 3 is inscribed in a sphere of radius 5. What is the difference between the volume of the sphere and the volume of the cylinder? The answer is 297.
Thanks!
The volume of the sphere is v = 4/3 π * r ^3 = 500π/3. The height of the cylinder is 2* sqrt(5^2 - 3^2) = 2*sqrt(25 - 9) = 8.
Volume of the cylinder = π * r^2 * h = π * 3^2 * 8 = 72π
The difference is 500π/3 - 72π = 297.4041
@aznboi4981 thanks for your reply. I understand everything except for the process you used to get 8 for the height. Can you please explain that?
(h/2)^2=5^2-3^2 (
Imagine a line from the center of the sphere to the center of the circle in the cylinder. This is h/2. The edge of the cylinder’s circle that touches the sphere (because it’s inscribed) is what used the radius’ measurement. Solve for h to get 8.