A solid right circular cone of height 20 cm and base radius 15 cm is melted and casted into smaller cones of equal sizes of height 5 cm and base radius 1.5 cm. Find how many cones are made.

The correct answer is: 4000

We have given the dimensions of two types of cones
For Cone 1
Radius, R = 15 cm
Height, H = 20 cm
For Cone 2
Radius, r = 1.5 cm
Height, h = 5 cm
We have to find the volume of the given cone
We know that
Volume of a cone 1 = ()πR²H

= ()(3.14)(15 x 15)(20)

= ()(3.14) (225 x 20)

= ()(3.14)(4500)

= 3.14 x 1500

= 47100 cm³

Volume of a cone 2 = ()πr²h

= ()(3.14)(1.5 x 1.5)(5)

= ()(3.14) (2.25 x 5)

= ()(3.14)(11.25)

= 3.14 x 3.75

= 11.775 cm³
Therefore number of cone 2 will be made from a single cone 1

= 47100 / 11.775

= 4000
Therefore, the number of cones is 4000
Therefore correct option is c) 4000