Question

find the surface area of the following cylinder.
a 20π cm²
b 24π cm²
c 32π cm²
d 36π cm²

Explanation:

Step1: Find the radius

The diameter is 4 cm, so the radius $r=\frac{4}{2}=2$ cm.

Step2: Calculate the area of the two bases

The area of one - circular base is $A_{base}=\pi r^{2}=\pi\times2^{2}=4\pi$ $cm^{2}$. The area of two bases is $A_{2bases}=2\times4\pi = 8\pi$ $cm^{2}$.

Step3: Calculate the lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Here, $r = 2$ cm and $h = 6$ cm, so $A_{lateral}=2\pi\times2\times6=24\pi$ $cm^{2}$.

Step4: Calculate the total surface area

The total surface area of the cylinder $A = A_{2bases}+A_{lateral}=8\pi + 24\pi=32\pi$ $cm^{2}$.

Answer:

C. $32\pi$ $cm^{2}$