Question

question 8 of 10 which of the following is the surface area of the right cylinder below? a. 72π units² b. 144π units² c. 192π units² d. 176π units²

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a right - cylinder is $S = 2\pi r^{2}+2\pi rh$, where $r$ is the radius and $h$ is the height. From the figure, $r = 8$ and $h = 3$.

Step2: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^{2}$. For two bases, $A_{2bases}=2\pi r^{2}=2\pi\times8^{2}=2\pi\times64 = 128\pi$.

Step3: Calculate the lateral - surface area

The lateral - surface area is $A_{lateral}=2\pi rh$. Substitute $r = 8$ and $h = 3$ into the formula: $A_{lateral}=2\pi\times8\times3=48\pi$.

Step4: Calculate the total surface area

$S=A_{2bases}+A_{lateral}=128\pi + 48\pi=176\pi$.

Answer:

D. $176\pi$ units$^{2}$