A regular hexagonal prism is inscribed in the cylinder. The height of the cylinder is 15 cm

| April 18, 2021 | education

A regular hexagonal prism is inscribed in the cylinder. The height of the cylinder is 15 cm, the diameter of its base is 48 cm. Calculate the area of the lateral surface of the prism.

Let us draw from the center of the circle of the base of the cylinder the segments OA and OB, the lengths of which are equal to the radius of the circle, then OA = OB = D / 2 = 48/2 = 24 cm.

Since at the base of the prism there is a regular hexagon, the chord AB contracts the arc, the degree measure of which is 360/6 = 60, then the central angle AOB = 60, and the triangle AOB is equilateral, AB = OA = OB = 24 cm.

The side surface of the prism consists of six identical rectangles ABB1A1, then S side = 6 * AB * AA1 = 6 * 24 * 15 = 2160 cm2.

Answer: The area of the lateral surface of the prism is 2160 cm2.



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