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# 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.

- 40
- 400
- 4000
- 4020

Hint:

### Volume of a cone = ()πr2h

## 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 = ()πR^{2}H

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

= ()(3.14) (225 x 20)

= ()(3.14)(4500)

= 3.14 x 1500

= 47100 cm^{3}

Volume of a cone 2 = ()πr^{2}h

= ()(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 cm^{3}

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

^{3}

^{2}h

^{3}

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

Therefore, the number of cones is 4000

Therefore correct option is c) 4000

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