Question

A circular shape metal sheet having radius 12 cm cut into 4 equal sectors. Using each
sector a cone is made up.
(a) What is the slant height of the cone?
(b)Find the base radius of the cone.

Answer 1

QUESTION: A circular shape metal sheet having radius 12 cm cut into 4 equal sectors. Using each

sector a cone is made up.

(a) What is the slant height of the cone?

(b)Find the base radius of the cone.

ANSWER:

Given the radius of circle 12cm

This becomes the slant height of cone  

The angle of sector 120°

 The length of arc is given as=  x/360 × 2πr

= 120/360 × 2 × π × 12

= 1/3 2π × 12

= 2π×4

= 8π

This become the circumference of base circle = 2πr = 8π

= 2r=8

= r=4

According to Pytagorous theorm

(Slantheight)²   =(height)²  +(radius)²

= 12²   =(height)² + 4²

= 144=(height)²   +16

= (height)²   =144−16

= (height)²   = 132

height=   √132

volume of cone=  1/3πr²  h

= 1/3 × 22/7 × 4 × 4 × √132

= 362√132/21

thanks for asking this question!

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