Question

question 4 of 10 which of the following is the surface area of the right cylinder below? 14 8 a. 204π units² b. 896π units² c. 224π units² d. 352π units²

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Identify values of $r$ and $h$

Given that $r = 8$ and $h = 14$.

Step3: Calculate the area of the two bases

The area of one base is $A_{base}=\pi r^2=\pi\times8^2 = 64\pi$. The area of two bases is $2\pi r^2=2\times64\pi = 128\pi$.

Step4: Calculate the lateral - surface area

The lateral - surface area is $A_{lateral}=2\pi rh=2\pi\times8\times14=224\pi$.

Step5: Calculate the total surface area

$S=2\pi r^2 + 2\pi rh=128\pi+224\pi=352\pi$.

Answer:

D. $352\pi$ units$^2$