Find the total surface area of an equilateral cylinder if the lateral surface area is 60n cm2

The lateral surface area of the cylinder is equal to the product of its height and the circumference of the base:

Sside = пd * h.

Hence:

d * h = S side / п = 60p / п = 60.

In an equilateral cylinder, the height is equal to the diameter of the base, which means:

d = h = √60 = 2√15 cm.

The base area is calculated by the formula:

Ssc = пr ^ 2, where r is the radius of the cylinder base.

The radius is half the diameter: r = d / 2 = 2√15 / 2 = √15 cm.

Sbn = п * (√15) ^ 2 = 15p cm2.

The total surface area of the cylinder is equal to the sum of the lateral surface areas and two bases:

Sful = S side + 2 * Sb = 60п + 2 * 15п = 90п cm2.