The diagram shows a cylinder with radius 8 cm inside a sphere with radius 17 cm.Both ends of the cylinder touch the curved surface of the sphere.(i) Show that the height of the cylinder is 30 cm.

To show that the height of the cylinder is 30 cm, we can use the Pythagorean theorem.

The sphere's radius is the hypotenuse of a right triangle, where one side is the radius of the cylinder and the other side is half of the height of the cylinder.

Given that the radius of the sphere is 17 cm and the radius of the cylinder is 8 cm, we can set up the following equation:

(17 cm)^2 = (8 cm)^2 + (1/2 * height of the cylinder)^2

289 cm^2 = 64 cm^2 + 1/4 * (height of the cylinder)^2

Subtract 64 cm^2 from both sides:

225 cm^2 = 1/4 * (height of the cylinder)^2

Multiply both sides by 4:

900 cm^2 = (height of the cylinder)^2

Take the square root of both sides:

30 cm = height of the cylinder

Therefore, the height of the cylinder is 30 cm.