What is the surface area of a cylinder whose end area is 11 and height is 11 rounded to the nearest whole number?

Answer 1

Imagine taking the ends off the cylinder, cutting the side down from end to end and unrolling the side; this creates a rectangle with the height of the cylinder along one edge and the circumference of the end along the other.

Thus area of side = circumference × height.

The ends of the cylinder are circles, thus:

area = π × radius²

→ radius = √(area ÷ π)

circumference = 2 × π × radius

→ circumference = 2 × π × √(area ÷ π) = 2 × √(area × π)

→ area side = 2 × √(area × π) × height

→ surface area of cylinder = 2 × area ends + area side

→ surface area = 2 × 11 units² + 2 × √(11 units² × π) × 11 units

→ surface area = 22 + 22 × √(11π) units²

→ surface area ≈ 22 + 129.33 units² ≈ 151 units²