Question

question 9 of 10 what is the surface area of the right cone below? a. 167π units² b. 176π units² c. 896π units² d. 224π units²

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cone is $S=\pi rl+\pi r^{2}$, where $r$ is the radius of the base and $l$ is the slant height.

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

From the figure, $r = 8$ and $l=14$.

Step3: Calculate the lateral - area and base - area

The lateral - area $A_{l}=\pi rl=\pi\times8\times14 = 112\pi$. The base - area $A_{b}=\pi r^{2}=\pi\times8^{2}=64\pi$.

Step4: Calculate the total surface area

$S = A_{l}+A_{b}=112\pi + 64\pi=176\pi$.

Answer:

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