The height of the cylinder is equal to the diameter of the base; the volume of the cylinder is 2n cm ^ 3.

| February 26, 2021 | education

The height of the cylinder is equal to the diameter of the base; the volume of the cylinder is 2n cm ^ 3. Find the total surface area of the cylinder.

The volume of a cylinder is equal to the product of the area of the base and the height of the cylinder.

Sosn = n * R ^ 2.

V = n * R ^ 2 * h.

Since, by condition, the height is equal to the diameter of the circle, then h = 2 * R.

Then V = n * R ^ 2 * 2 * R = 2 * n * R ^ 3 = 2 * n.

R3 = 1.

R = 1 cm.

Then h = 2 * R = 2 cm.

Determine the area of the base of the cylinder.

Sax = n * R ^ 2 = n cm2.

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

Side = 2 * n * R * h = 2 * n * 1 * 2 = 4 * n cm2.

Let us determine the total surface area.

Spol = 2 * Sb + S side = 2 * n + 4 * n = 6 * n cm2.

Answer: The total surface area of the cylinder is 6 * n cm2.



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