Question

calculate the surface area of a cylinder with diameter 4 m and height 0.5 m.
a) 25 m²
b) 37 m²
c) 31 m²
d) 113 m²

Explanation:

Step1: Find the radius

Given diameter $d = 4$ m, radius $r=\frac{d}{2}=\frac{4}{2}=2$ m.

Step2: Calculate the base - area

The area of each base of the cylinder is $A_{base}=\pi r^{2}$, with $\pi\approx3.14$ and $r = 2$ m, so $A_{base}=3.14\times2^{2}=3.14\times4 = 12.56$ m².

Step3: Calculate the lateral - area

The lateral - area formula is $A_{lateral}=2\pi rh$, where $h = 0.5$ m and $r = 2$ m. So $A_{lateral}=2\times3.14\times2\times0.5=6.28$ m².

Step4: Calculate the surface - area

The surface - area of a cylinder $A = 2A_{base}+A_{lateral}$. Substitute the values: $A=2\times12.56 + 6.28=25.12+6.28 = 31.4\approx31$ m².

Answer:

c) 31 m²