SOLUTION: from a circular sheet of paper of radius 25 cm a sector area 4% is removed. if the remaining part is used to make a conical surface then the ratio of the radius and height of cone
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Question 898348: from a circular sheet of paper of radius 25 cm a sector area 4% is removed. if the remaining part is used to make a conical surface then the ratio of the radius and height of cone? Answer by Theo(13342) (Show Source):
if you cut out a sector that represents 4% of the area, then you are left with 96% of the area.
that becomes the lateral surface area of the cone.
it's your piece of paper that has had a pie shaped slice taken out and then folded until the ends of the cut out piece touch again. this is what causes the height to form.
if you cut out 4% of the area to form a sector, then you are effectively cutting out 4% of the circumference as well since the exterior of the sector is the length of the arc of the sector that lays on the circumference of the circle.
the number of central degrees of the sector that you are cutting out is equal to 4% of 360 degrees which is equal to 14.4 degrees.
area of sector = 14.4 / 360 * pi * 25^2 = 78.53...
area of original circle is pi*25^2 = 1963.49...
area that is left is 1884.95...
this becomes the area of the lateral surface area of the cone.
if the angle of the sector is 14.4 degrees, then the angle of the arc formed by the sector is the same 14.4 degrees.
the length of this arc is equal to 14.4 / 360 * 2 * pi * 25 = 6.283185307...
the original circumference of the circle on the piece of paper, before cutting out the sector, is 2 * pi * 25 = 157.079632679...
the difference is equal to 150.796447372...
this is the circumference of the base of the cone.
the radius of the base of the cone is therefore equal to 150.796447372 / (2*pi) which is equal to 24.
now you take a cross section and you get a base of 24 and a hypotenuse of 25 which leads to a height of 7 through the use of the pythagorean formula of base squared plus height squared equals hypotenuse squared.
that's your solution.
the height of the cone is 7.
the base of the cone has a radius of 24.
the slant height of the cone is 25.
the question is:
if the remaining part is used to make a conical surface then the ratio of the radius and height of cone?
i believe they are talking about the original radius which is the slant height of the cone.
the height is equal to 7.
the ratio of the slant height to the height is 25/7.
the ratio of the height to the slant height is 7/25.
the ratio of the radius of the base to the height is equal to 24/7.
the ratio of the height to the radius of the based is equal to 7/24.
i believe you're looking for 25/7 or 7/25 because 25 is the original radius that became the slant height of the cone and is also the radius of the conical surface that was formed after taking out the sector, meaning it's the piece that remained.
formulas for a cone are:
the following pictures might help visualizing what i am talking about.
