The sides of the rectangle, which is a scan of the lateral surface of the cylinder, are equal to 24 pi cm and 16 cm

| January 7, 2021 | education

The sides of the rectangle, which is a scan of the lateral surface of the cylinder, are equal to 24 pi cm and 16 cm (the height of the cylinder). Calculate: a) the length of the radius of the base of the cylinder b) the length of the diagonal of the axial section of the cylinder c) the total surface area of the cylinder.

The length of the ABP rectangle AВСD is the circumference at the base of the cylinder.
Then L = 24 * π = 2 * π * R.
R = 24 * π / 2 * π = 12 cm.
The diagonal section of the cylinder is the rectangle AMEC, then its diagonal, according to the Pythagorean theorem, is: AE2 = AK2 + EK2 = (2 * R) 2 + EK2 = 576 + 256 = 832.
AE = 8 * √13 cm.
Determine the area of the base of the cylinder.
Sb = π * R2 = 144 * π cm2.
Let us determine the area of the lateral surface of the cylinder.
S side AB * BC = 16 * 24 * π = 384 * π cm2.
Then Sпов = 2 * Sсн + S side = 288 * π + 384 * π = 672 * π cm
Answer: The radius is 12 cm, the diagonal is 8 * √13 cm, the area is 672 * π cm2.



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