Math, asked by surya9578, 9 months ago

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

Answered by amitnrw
4

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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