A cylinder is inscribed in a regular triangular prism. Find its surface area if the side of the base

| April 24, 2021 | education

A cylinder is inscribed in a regular triangular prism. Find its surface area if the side of the base of the prism is 3 √ 3 and the height is 4.

The bases of the cylinder inscribed in a regular prism are circles inscribed in equilateral triangles ABC and A1B1C1.

The radius of the inscribed circle is determined by the formula: R = a * √3 / 6, where a is the side length of a regular triangle. R = 3 * √3 * √3 / 6 = 9/6 = 3/2 cm.

The height of the inscribed cylinder is equal to the height of the prism.

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

Sb = n * R2 = n * 9/4 cm2.

Determine the circumference at the base of the cylinder.

L = 2 * n * R = 2 * n * 3/2 = 3 * n cm.

Then S side = L * CC1 = 3 * n * 4 = 12 * n cm2.

Sпов = 2 * Sсн + S side = 2 * n * 9/4 + 12 * n = n * (9 + 24) / 2 = 16.5 * n cm2

Answer: The area of ​​the cylinder is 16.5 * n cm2



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