1. ## Cone Problem

Hi All,

The problem below shows a sector of a circle on the right hand side and when it is folded it makes the cone on the left. Find the arc length.

I started of by finding the slant height or radius:

$\displaystyle \sqrt{10^2 + 6^2} = 11.7$

To find arc length i have the formula:
$\displaystyle \frac{\theta}{360} \times 2\pi r$

But, How do i find the angle in the unfolded sector?

I tried finding the the angle of the top part of the cone using:
$\displaystyle tan\theta = \frac{6}{10} = 31 \times 2 = 62$

Then, 360 - 62 = 329 But, this input into the arc-length formula is not the

2. ## Re: Cone Problem

Originally Posted by BobBali
Hi All,

The problem below shows a sector of a circle on the right hand side and when it is folded it makes the cone on the left. Find the arc length.

I started of by finding the slant height or radius:

$\displaystyle \sqrt{10^2 + 6^2} = 11.7$

To find arc length i have the formula:
$\displaystyle \frac{\theta}{360} \times 2\pi r$

But, How do i find the angle in the unfolded sector?

I tried finding the the angle of the top part of the cone using:
$\displaystyle tan\theta = \frac{6}{10} = 31 \times 2 = 62$

Then, 360 - 62 = 329 But, this input into the arc-length formula is not the
Obviously the arc length equals the circumference of the base area:

$\displaystyle c_{base} = 2 \cdot \pi \cdot 6$

If (and only if) you want to to know the central angle of the sector you have to determine the length of s using Pythagorean theorem. Then use the proportion:

$\displaystyle \frac{\theta}{360^\circ}=\frac{2 \cdot \pi \cdot 6}{2 \cdot \pi \cdot s}$

Solve for $\displaystyle \theta$.

### cone unfolded formula

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