The height of the cone is 15 cm and the generatrix of the cone is 20 cm. Find the radius of the cone.

It is known:
Cone;
Cone height = 15 cm;
Cone generatrix = 20 cm.
Find the radius of the cone.
Decision:
Consider a right-angled triangle ABC, where:
Angle C = 90 °;
AB – generatrix of the cone and hypotenuse of the triangle = 20 cm;
AC – the height of the cone and leg of the rectangle = 15 cm;
ВС = R – rectangle leg and cone radius.
We get:
R = √ (20 ^ 2 – 15 ^ 2) = √ ((20 – 15) * (20 + 15)) = √ (5 * 35) = √ (5 * 5 * 7) = √ (25 * 7) = √25 * √7 = 5√7;
As a result, we got that the radius of the cone is R = 5√7.
Answer: R = 5√7.