two metallic right circular cones having their heights 4 1 cm and..., Area & Volume, General Mathematics

Question:Two metallic right circular cones having their heights `4.1` cm and `4.3` cm and the radii of their bases `2.1` cm each, have been melted together and recast into a sphere. The diameter of the sphere is :

A `4.2 cm` 
B `1.4 cm` 
C `3.5 cm` 
D `6.3 cm`

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+ AnswerA

+ ExplanationVolume of `2`cones 

`= [1/3 π xx (2.1)^2 xx 4.1 + 1/3 π xx (2.1)^2 xx 4.3] cm^3.`

`= 1/3 π xx (2.1)^2 (8.4) cm^3.`

Volume of sphere 

`= 1/3 π xx (2.1)^2 (8.4) cm^3.`

`:. 4/3 π R^3`

`= 1/3 π (2.1)^3 .4`

`or R = 2.1 cm.`

`:. 4/3 π R^3`

:. Diameter of the sphere 

`= 4.2 cm.`

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