a cone is made from a metal sheet in the form of a sector of a circle ..If the radius of the circle is 14 cm and the sector angle is 60⁰, find the radius of the base ,slant height and height of the cone formed
Answers
Given : a cone is made from a metal sheet in the form of a sector of a circle .radius of the circle is 14 cm and the sector angle is 60⁰,
To Find : the radius of the base ,slant height and height of the cone formed
Solution:
cone is made from a metal sheet in the form of a sector of a circle
Arc length of sector would be the circumference of the base of the cone
Radius of circle would be the slant height
Radius of circle = 14 cm
Sector angle = 60°
Arc length = ( 60/360) 2π(14) = 14π/3
radius of the base of cone = r
circumference = 2πr
2πr = 14π/3
=> r =7/3 cm
Radius = 7/3 cm
Slant height = 14 cm
Height of cone = √14² - (7/3)²
= 7√2² - (1/3)²
= 7√4 -1/9
= (7/3)√35
radius of the base = 7/3 cm
,slant height = 14 cm
height of the cone = (7/3)√35 = 13.8 cm
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