The radius of the base of the cylinder is 6cm, and the height is 5cm. Find the diagonal of the axial section of the cylinder.

Given: cylinder, height AB = 5 cm, R = AO = OD = 6 cm, axial section ABCD.

Find: BD =? cm.

Solution: the diagonal of the axial section BD forms a right-angled triangle ABD with the height of the cylinder AB and the side of the section AD (where the angle A is straight, AB and AD are the legs, BD is the hypotenuse).

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs:

BD ^ 2 = AB ^ 2 + AD ^ 2.

Find AD = AO + OD = 6 + 6 = 12 cm and substitute:

BD ^ 2 = 5 ^ 2 + 12 ^ 2,

BD ^ 2 = 25 + 144,

BD ^ 2 = 169,

BD = root of 169 = 13 cm.

Answer: BD = 13 cm.