The diagonal of the axial section of the cylinder is 26 cm, the height of the cylinders is 24 cm. Calculate the area of the cylinder.
The diagonal section of the cylinder is the rectangle ABCD, then the triangle ACD is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg AD.
AD ^ 2 = AC ^ 2 – CD ^ 2 = 676 – 576 = 100.
AD = 10 cm.
AD is the diameter of the base of the cylinder, then R = AD / 2 = 10/2 = 5 cm.
Determine the area of the base of the cylinder.
Sb = π * R ^ 2 = π * 25 cm2.
Let us determine the area of the lateral surface of the cylinder.
Side = 2 * π * R * AB = 2 * π * 5 * 24 = π * 240 cm2.
Then Sпов = 2 * Sсн + S side = 50 * π + 240 * π = 290 * π cm2.
Answer: The surface area of the cylinder is 290 * π cm2.
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