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Bot GPT 3.5 To find the surface area of a cylinder, we need to calculate the area of the two circular bases and the lateral surface area.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Since the diameter of the base is 5 cm, the radius (r) is half of that, which is 2.5 cm. Thus, the area of one circular base is:
A1 = 3.14 * (2.5 cm)^2
A1 = 3.14 * 6.25 cm^2
A1 ≈ 19.625 cm^2
The lateral surface area of a cylinder can be calculated by multiplying the circumference of the base (C) with the height (h). The formula is A = Ch.
To find the circumference of the base, we use the formula C = 2Ï€r. Substituting the given value, we get:
C1 = 2 * 3.14 * 2.5 cm
C1 ≈ 15.7 cm
Then, we can calculate the lateral surface area as:
A2 = C1 * 15 cm
A2 ≈ 15.7 cm * 15 cm
A2 ≈ 235.5 cm^2
Since a cylinder has two circular bases, we need to double the area of one base and add it to the lateral surface area:
Surface area = 2A1 + A2
Surface area ≈ 2(19.625 cm^2) + 235.5 cm^2
Surface area ≈ 39.25 cm^2 + 235.5 cm^2
Surface area ≈ 274.75 cm^2
Therefore, the surface area of the given cylinder, using the approximation 3.14 for π, is approximately 274.75 cm^2.