The diameter of the base of the cone is 30, and the length of the generatrix is 17. Find the height of the cone.

h = √ (l ^ 2 – r ^ 2) (known formula);

l = 17 (by condition);

d = 30;

d = 2r;

r = d / 2 = 30/2 = 15;

h = √ (17 ^ 2 – 15 ^ 2) = √ (289 – 225) = √ (64);

h = 8.

Answer: 8.

Explanation: If you build a cone and draw the height and radius, then they form a right-angled triangle. Using the Pythagorean theorem, we write down the formula for finding the height.