The axial section of the cylinder is square. calculate the ratio of the total surface area of the cylinder to the area of its base.
| February 1, 2021 | education
If the axial section of the cylinder is a square, then the diameter of the base of the cylinder d is equal to the height of the cylinder h. Let’s introduce the notation: h = d = a.
The lateral surface area is equal to the product of the base circumference times the cylinder height:
Sside = πa * a = πa ^ 2.
Base area:
Sbn = πа ^ 2/4.
The total surface area is equal to the sum of the lateral surface areas and the two bases:
S full = S side + 2 * S main = πa ^ 2 + 2 * πа ^ 2/4 = 3πа ^ 2/2.
Total surface area to base area ratio:
Sful / Sbn = (3πа ^ 2/2) / (πа ^ 2/4) = 6.
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