Question

the surface area of this cone is 1,431.84 square feet. what is the slant height of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 12 ft s ≈ 26.00 feet

Explanation:

Step1: Recall cone surface - area formula

The surface - area formula of a cone is $A=\pi r(r + l)$, where $A$ is the surface area, $r$ is the radius, and $l$ is the slant height. Given $A = 1431.84$ square feet and $r = 12$ feet, and $\pi\approx3.14$. Substitute the values into the formula: $1431.84=3.14\times12\times(12 + l)$.

Step2: Simplify the left - hand side of the equation

First, calculate $3.14\times12 = 37.68$. The equation becomes $1431.84=37.68\times(12 + l)$.

Step3: Solve for $(12 + l)$

Divide both sides of the equation by $37.68$: $\frac{1431.84}{37.68}=12 + l$. Since $\frac{1431.84}{37.68}=38$, the equation is $38 = 12 + l$.

Step4: Solve for $l$

Subtract 12 from both sides of the equation: $l=38 - 12$. So, $l = 26.00$ feet.

Answer:

$26.00$ feet