The height of the cylinder is 7 cm. The axial section diagonal makes an angle of 45 degrees.

| September 24, 2021 | education

The height of the cylinder is 7 cm. The axial section diagonal makes an angle of 45 degrees. with the plane of the base. Find the total surface area of the cylinder.

Since the diagonal of the axial section makes an angle of 450 with the base plane, then in the ABC triangle the angle ACB = 180 – 90 – 45 = 450. Since the angles at the base of the AC are equal, the ABC triangle is isosceles, AB = BC = 7 cm.

AB is the diameter of the circle at the base of the cylinder, then OA = R = AB / 2 = 7/2 = 3.5 cm.

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

Sop = n * R2 = n * 12.25cm2.

Let us determine the area of ​​the lateral surface of the cylinder.

Side = 2 * n * R * BC = 2 * n * 3.5 * 7 = n * 49 cm2.

Let us determine the total surface area of ​​the cylinder.

S floor = 2 * Sb + S side = 2 * n * 12.25 * n * 49 = n * 73.5 cm2.

Answer: The total surface area is n * 73.5 cm2.



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