SOLUTION: A sector with an angle 110 degrees at the center of a circle is cut away from a circular piece of paper of radius 70cm. The remaining part is folded to form a cone. Find 1. the ver

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Question 1183412: A sector with an angle 110 degrees at the center of a circle is cut away from a circular piece of paper of radius 70cm. The remaining part is folded to form a cone. Find 1. the vertical angle of the cone 2. The angle of the sector.

Found 5 solutions by mananth, ikleyn, CPhill, n2, n3:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
Length of arc =
length of arc p = 110/360 (2*pi*70)
p= 1540/36 * pi
area of major arc = (140 *pi -(1540/36)*(pi))
= 97.2 *pi
The area of major arc is the circumference of the base of cone
97.2*pi = d *pi
d= 97.2
r = 48.6
Now the radius of the circle becomes the slant height of the cone
height of cone
height of cone =
height of cone = 50.37
we know radius and height angle of cone can be calculated

Answer by ikleyn(53575)   (Show Source):
You can put this solution on YOUR website!
.
A sector with an angle 110 degrees at the center of a circle is cut away from a circular piece of paper of radius 70cm.
The remaining part is folded to form a cone. Find 1. the vertical angle of the cone 2. The angle of the sector.

After cutting away the sector of 110°, the remaining pert of the circle is the sector of 360° - 110° = 250°. The length of the arc of the sector of (250°, R = 70 cm) is = = 305.4323611 cm. The radius of the base of the cone 'r' can be defined from = 305.4323611, r = = 48.61111... cm. It is the same as to use equation = , r = = = 48.61111... cm. Now the cone has the slant height of 70 cm and the radius of 48.61111... cm. From the right-angled triangle, for the angle 'a' between the slant height and the cone axis we have sin(a) = = 0.694444... Thus angle 'a' is a = arcsin(0.694444), or about 44°. Vertical angle of the cone is about 2*44° = 88°.

Solved.

Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website!
Length of arc = +%28%28theta%29%2F360%29%2A+%28pi%29%2Ad%29
length of arc p = 110/360 (2*pi*70)
p= 1540/36 * pi
area of major arc = (140 *pi -(1540/36)*(pi))
= 97.2 *pi
The area of major arc is the circumference of the base of cone
97.2*pi = d *pi
d= 97.2
r = 48.6
Now the radius of the circle becomes the slant height of the cone
height of cone h=+sqrt%28l%5E2-r%5E2%29
height of cone = sqrt%2870%5E2-48.6%5E2%29
height of cone = 50.37
we know radius and height angle of cone can be calculated

Answer by n2(49)   (Show Source):
You can put this solution on YOUR website!
.
A sector with an angle 110 degrees at the center of a circle is cut away from a circular piece of paper
of radius 70cm. The remaining part is folded to form a cone. Find
1. the vertical angle of the cone
2. The angle of the sector.
~~~~~~~~~~~~~~~~~~~~~~~~~~~

This post by @CPhill is a copy-paste of the post by @mananth.

They both are very suspicious, because they both contain this phrase
"The area of major arc is the circumference of the base of cone".

As you see this gibberish, you should throw this solution to a garbage box
immediately without any doubts - it does not deserve further consideration.

In addition, the solution in both their posts are incomplete.

In my post (as @ikleyn) at this spot, I gave another, fully correct and complete solution to this problem,
So, you can disregard both posts by @mananth and by @CPhill.

Don't let them cloud your brain with flawed "quasi"-solutions.

Answer by n3(7)   (Show Source):
You can put this solution on YOUR website!
.

        To the managers of this project !
    Attention !!     Attention !!     ATTENTION !!

Today, I had a chance to review the bunch of solutions produced by @CPhill to Math problems at this forum.

               A list of the links follows

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1182443.html

https://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.244998.html

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1182444.html

https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1210543.html

https://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.1182591.html

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1182886.html

https://www.algebra.com/algebra/homework/playground/test.faq.question.1183412.html

https://www.algebra.com/algebra/homework/playground/test.faq.question.1210545.html

https://www.algebra.com/algebra/homework/Systems-of-equations/Systems-of-equations.faq.question.1210543.html

https://www.algebra.com/algebra/homework/formulas/Geometric_formulas.faq.question.1201106.html

My impressions about his skills as a developer of the AI for solution of school Math problems are at very low level.

This person has no necessary knowledge and understanding Math to work on the AI project
in the area of solution of Math problems.

He doesn't know what kinds of mathematical problems are possible and which ones are not.
He also doesn't know what kinds of solutions to mathematical problems are possible,
and which ones are not and should not be.

Very often he posts nonsense to the forum under the guise of mathematical problems,
and very often he posts nonsense to the forum under the guise of solutions to mathematical problems.

He also has no necessary skills to work in such a project NEITHER as an individual NOR as a member of a team.
For the team work, he has no necessary respect to the work of specialists in this area.

So, if you, the managers, want to continue such a project successfully, you should consider replacing this person
to a more appropriate candidate.

Yours well-wisher, @ikleyn