- - T NOT TO SCALE The diagram shows a cylinder with radius 8 cm inside a sphere with radius 17cm. Both ends of the cylinder touch the curved surface of the sphere. (i) Show that the height of the cylinder is 30 cm.

To find the height of the cylinder, we can consider the right triangle formed by the radius of the sphere (17 cm), the height of the cylinder (h), and the radius of the cylinder (8 cm).

Using the Pythagorean theorem, we have:

(radius of sphere)^2 = (radius of cylinder + height of cylinder)^2 + (radius of cylinder)^2

Substitute the given values:

17^2 = (8 + h)^2 + 8^2

289 = (8 + h)^2 + 64

Subtract 64 from both sides:

225 = (8 + h)^2

Take the square root of both sides:

15 = 8 + h

Subtract 8 from both sides:

h = 15 - 8

h = 7

Therefore, the height of the cylinder is 7 cm. This means the given height of the cylinder being 30 cm is incorrect.

- - T NOT TO SCALE The diagram shows a cylinder with radius 8 cm inside a sphere with radius 17cm. Both ends of the cylinder touch the curved surface of the sphere. (i) Show that the height of the cylinder is 30 cm. ​

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- - T NOT TO SCALE The diagram shows a cylinder with radius 8 cm inside a sphere with radius 17cm. Both ends of the cylinder touch the curved surface of the sphere. (i) Show that the height of the cylinder is 30 cm.