Question

what is the surface area of this cone? round your answer to the nearest hundredth. 14 m 12 m square meters

Explanation:

Step1: Find the radius

The diameter is 12 m, so the radius $r=\frac{12}{2}=6$ m.

Step2: Recall the surface - area formula

The surface - area formula of a cone is $A = \pi r(r + l)$, where $r$ is the radius and $l$ is the slant height. Here, $l = 14$ m and $r = 6$ m.

Step3: Substitute values into the formula

$A=\pi\times6\times(6 + 14)$.
First, calculate the sum inside the parentheses: $6+14 = 20$.
Then, $A=\pi\times6\times20=120\pi$.

Step4: Calculate the numerical value

Using $\pi\approx3.14159$, $A\approx120\times3.14159 = 376.9908$.
Rounding to the nearest hundredth, $A\approx376.99$ square meters.

Answer:

376.99