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A right circular cone is $5.4 cm$ high and radius of its base is $2 cm .$ It is melted and recast into another right circular cone with radius of base as $1.5 cm$ . What is the height of the new cone formed?

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8.2 cm

9.6 cm

19.1 cm

6.5 cm

answer is B.

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Detailed Solution

Given- height of the right circular cone =

5.4 cm

and radius of its base is

2 cm .

Radius of the new right circular cone = 1.5 cm.
The height of the new cone formed can be calculated using the formula,

Volume of cone = 13 π r 2 h

Volume of new cone = volume of old cone . 13 × 227 × (1.5) 2 h = 13 × 227 × (2) 2 × (5.4) 2.25 h = 4 × 5.4 h = 4 × (5.4) 2.25 h = 9.6 cm

Therefore, the height of the new cone is 9.6cm.
Hence, option 2 is the correct option.

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