The chord of the base of the cylinder is 12 cm and is 8 cm from the center of this base.

| August 6, 2021 | education

The chord of the base of the cylinder is 12 cm and is 8 cm from the center of this base. The segment connecting the center of the other base of the cylinder with the middle of the given chord forms an angle of 45 degrees with the base plane. Find the volume of the cylinder.

From the center of the circle of point O, draw the radii OA and OB. Triangle OAB is isosceles, then its height OH is also the median of the triangle, then AH = BH = AB / 2 = 12/2 = 6 cm.

In a right-angled triangle AOH, according to the Pythagorean theorem, we determine the length of the hypotenuse OA.

OA ^ 2 = AH ^ 2 + OH ^ 2 = 36 + 64 = 100.

ОА = R = 10 cm.

In a right-angled triangle OO1H, one of the acute angles is 450, then the legs of this triangle are equal. OH = OO1 = 8 cm.

Determine the area of ​​the base of the cylinder.

Sb = π * R ^ 2 = π * 100 cm2.

Determine the volume of the cylinder.

S = Sosn * OO1 = π * 100 * 8 = 800 * π cm3.

Answer: The volume of the cylinder is 800 * π cm3.



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