Question

the surface area of the following cylinder is (\text{____}pi cm^{2}).

Explanation:

Step1: Identify the radius and height

The diameter is 6 cm, so the radius $r=\frac{6}{2}=3$ cm and height $h = 10$ cm.

Step2: Calculate the two - base areas

The area of one base is $A_{base}=\pi r^{2}=\pi\times3^{2}=9\pi$ cm². The area of two bases is $A_{2bases}=2\times9\pi = 18\pi$ cm².

Step3: Calculate the lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi rh$. Substitute $r = 3$ cm and $h = 10$ cm, we get $A_{lateral}=2\pi\times3\times10=60\pi$ cm².

Step4: Calculate the total surface area

The total surface area $A = A_{2bases}+A_{lateral}=18\pi + 60\pi=78\pi$ cm².

Answer:

$78$