SOLUTION: please help me solve this quest ion ((( a cone whose base diameter and vertical height are 24cm and 5cm respectively is unfolded to form a sector of circle. calculate (i)the radiu

Question 1135675: please help me solve this quest
ion ((( a cone whose base diameter and vertical height are 24cm and 5cm respectively is unfolded to form a sector of circle. calculate (i)the radius of circle (ii) the angle of sector.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the base diameter of the cone is 24 centimeters, then the base radius of the cone is 12 centimeters and the circumference of the base is equal to 2 * pi * 12 = 24 * pi centimeters

if the vertical height of the cone is 5 centimeters and the base radius of the cone is 12 centimeters, then the slant height of the cone is sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13 centimeters

when you unfold the cone to make a sector, the sector has an arc length that is the circumference of the base of the cone which makes it equal to 24 * pi centimeters with a radius of 13 centimeters because the radius of the sector is the slant height of the cone.

the full circle with a radius of 13 centimeters is equal to 2 * pi * r = 2 * pi * 13 = 26 * pi.

the sector arc is 24 * pi and the circle circumference is 26 * pi, so the angle of the sector has to be (360 * 24 * pi) / (26 * pi) = 360 * 24 / 26 = 332.3076923 degrees.

your solution is that the angle of the sector is 332.3076923 degrees.

i confirmed this to be true by using a cone calculator and providing it with a base radius of 12 and a cone height of 5.

it came back with a sector angle (S) of 332.307692 degrees which is the same as 332.3076923 degrees if you round it to 6 decimal digits.

here's the cone calculator i used.

http://www.cleavebooks.co.uk/scol/calcone.htm

here's the results of the analysis using that calculator.

$$$

click on the link for the calculator to get the full instructions and information.

the S angle is the angle of the sector.

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