Q3 of 35 Page 200

What is the ratio of the base – radius and slant height of a cone made by rolling up a semicircle?

Here, The sector is a semicircle

Let rs be the radius of the sector.


Then slant height of the cone will be rs.


Central angle θ of a semi circle = 180°


The arc length of a semicircle is 'half the circumference of the full circle'


The 'circumference of the full circle' is 2πrs.


So half of it is πrs.


This is same as the circumference of the base of the cone


So if rb is the radius of the base of the cone,


2πrb = πrs



But rs is the slant height.



More from this chapter

All 35 →
1

What are the radius of the base and slant height of a cone made by rolling up a sector of central angle 60° cut out from a circle of radius 10 centimetres?

 2

What is the central angle of the sector to be used to make a cone of base radius 10 centimetres and slant height 25 centimetres?

 1

What is the area of the curved surface of a cone of base radius 12 centimetres and slant height 25 centimetres?

 2

What is the surface area of a cone of base diameter 30 centimetres and height 40 centimetres?