Mathematics, 10.01.2020 06:31 samanthashade8352

Aconical paper funnel of radius 4 and height 6 units is needed to make a good cup of coffee. if this funnel is made out of a sector of a circle, what must be the radius of this circle and what must be central angle of the sector?

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The radius of this circle is $2\sqrt{13}$ and the central angle of the sector is $\theta=\frac{2}{\sqrt{13}}\times360^\circ$ .

Step-by-step explanation:

Consider the provided information.

If a conical paper funnel is made out of a sector of circle then the radius of the sector becomes the slant height of the cone, and the length of the curved part of the sector becomes the circumference of the base of the cone.

First find the slant height: $l=\sqrt{r^2+h^2}$

$l=\sqrt{4^2+6^2}$

$l=\sqrt{16+36}$

$l=2\sqrt{13}$

Thus, the radius of the sector is $2\sqrt{13}$ which is same as the slant height of the cone.

Now, the circumference of the base of the cone is same as the length of the curved part.

$C=2\pi r$

$C=2\pi \times4=8\pi$

The length of the curved part = $\frac{\theta}{360\circ}\times2\pi r$

$\frac{\theta}{360\circ}\times2\pi \times2\sqrt{13}=8\pi$

$\frac{\theta}{360\circ}\times\sqrt{13}=2$

$\theta=\frac{2}{\sqrt{13}}\times360^\circ$

Hence, the radius of this circle is $2\sqrt{13}$ and the central angle of the sector is $\theta=\frac{2}{\sqrt{13}}\times360^\circ$ .

Answer from: Quest

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

In the figure below abd measures 37 degrees what is the measure of abc?

Answer from: Quest

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

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of home video projects.

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"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

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rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

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cd sales totaled 10.7 million units

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sales for calendar 1987 will reach 20

(continued on page 79)

step-by-step explanation:

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Aconical paper funnel of radius 4 and height 6 units is needed to make a good cup of coffee. if this...

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