Question

what is the surface area of this cone? round your answer to the nearest hundredth. 14.6 ft 9 ft square feet

Explanation:

Step1: Identify the formula for surface area of a cone

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

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

From the figure, $r = 9$ feet and $l=14.6$ feet.

Step3: Substitute the values into the formula

$A=\pi\times9\times(9 + 14.6)$.
First, calculate the sum inside the parentheses: $9+14.6 = 23.6$.
Then, $A=\pi\times9\times23.6=212.4\pi$.

Step4: Calculate the numerical value

Using $\pi\approx3.14159$, $A\approx212.4\times3.14159 = 667.273616$.

Step5: Round to the nearest hundredth

Rounding $667.273616$ to the nearest hundredth gives $A\approx667.27$ square feet.

Answer:

$667.27$