Question

the surface area of this cone is 37.68 square centimeters. what is the slant height of this cone? round your answer to the nearest hundredth. 2 cm s ≈ centimeters

Explanation:

Step1: Recall 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 $A = 37.68$ square centimeters and $r = 2$ centimeters.

Step2: Substitute values into the formula

Substitute $A = 37.68$ and $r = 2$ into $A=\pi r(r + l)$:
$37.68=\pi\times2\times(2 + l)$
Since $\pi\approx3.14$, we have $37.68 = 3.14\times2\times(2 + l)$.
First, calculate $3.14\times2=6.28$. So the equation becomes $37.68 = 6.28\times(2 + l)$.

Step3: Solve for $l$

Divide both sides of the equation $37.68 = 6.28\times(2 + l)$ by $6.28$:
$\frac{37.68}{6.28}=2 + l$
$6=2 + l$.
Subtract 2 from both sides: $l=6 - 2=4$.

Answer:

$4.00$