Find the total surface area of an equilateral cylinder if the lateral surface area is 60n cm2
February 7, 2021 | education
| 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.
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