Q2 of 35 Page 200

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?

Given that slant height of the cone should be 25 cm.

So radius of the sector rs = 25 cm


To find: Central angle θ


Radius of the base rb = 10 cm


So circumference of the base = 2πrb = 2π×10 = 20π cm ..(1)


This circumference is equal to the length of the arc


The length of arc will be


Thus, the length of arc will be . …(2)


Equating the results in (1) and (2):



⇒ θ = 144°


More from this chapter

All 35 →
7

What is the surface area of a square pyramid of base perimeter 64 centimetres and volume 1280 cubic centimetres?

 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?

 3

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

 1

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