Answer: the height of the cylinder is 24
Explanation:
The formula for determining the total surface area of a cylinder is expressed as
Total surface area = 2πr² + 2πrh
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
From the information given,
Total surface area = 56π
radius = 2
Therefore,
56π = (2 × π × 2²) + 2 × π × h
56π = 8π + 2πh
56 × 3.14 = (8 × 3.14) + (2 × 3.14 × h)
175.84 = 25.12 + 6.28h
6.28h = 175.84 - 25.12 = 150.72
h = 150.72/6.28
h = 24