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A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 2 inches and a height of 6 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 4 inches.
What will the height of the new cones be?

Respuesta :

metchelle
The formula for the volume of a right circular cone is V = [tex] \pi r^{2} h[/tex]. In solving for the volume of the first french fries cones V = [tex] \pi ( 2^{2} )(6)[/tex] = 75.398 [tex] in^{3} [/tex]. In solving for the height of the second french fries cones with a new radius of 4, the formula is rearranged to h =[tex] \frac{V}{ \pi r^{2} } [/tex] = [tex] \frac{75.398}{ \pi (4^{2}) } [/tex] = 1.5 in or inches. The height of the new cones will be 1.5 inches.
aksnkj

A cone is melted and converted into a new cone. 1.5 inch is the height of the new cones.

Given,

The radius of old cone is 2 inches.

The height of old cone is 6 inches.

The radius of new cone is 4 inches.

What is the volume of cones?

Now the volume of old cone will be,

[tex]V=\frac{1}{3}\pi \times r^{2} \times h[/tex]

[tex]V=\dfrac{1}{3} \times 3.14\times 2^2\times 6[/tex]

[tex]V=8\times 3.14[/tex]

Since the volume of old cone and new cone will be the same,

so volume of new cone will be,

[tex]3.14\times 8=\dfrac{1}{3}\times 3.14\times 4^2\times h[/tex]

[tex]8\times 3=16\times h[/tex]

[tex]h=\dfrac{24}{16}[/tex]

[tex]h=1.50\ inches[/tex]

Hence the height of the new cones will be 1.5 inch.

For more details about cones, follow the link:

https://brainly.com/question/1315822

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