Three spherical balls of radii 1 cm, 2 cm and 3 cm are melted to form a single spherical ball. In the process, the loss of material is 25%. The radius of the new ball is

6 cm

5 cm

3 cm

3 cm

3 cm

Material lost = 25% = $1 fourth$
Remaining material = $open parentheses 1 minus 1 fourth close parentheses space equals space 3 over 4$
Volume of the new ball
$equals space 3 over 4 space cross times space 4 over 3 straight pi open parentheses straight r subscript 1 cubed space plus space straight r subscript 2 cubed space plus space straight r subscript 3 cubed close parentheses space equals space straight pi left parenthesis 1 cubed space plus space 2 cubed space plus space 3 cubed right parenthesis space equals space straight pi left parenthesis 1 space plus space 8 plus space 27 right parenthesis space equals space 36 space straight pi space cm cubed$

$therefore space space space space space 4 over 3 πr cubed space equals space 36 straight pi rightwards double arrow space space space straight r cubed space equals space fraction numerator 36 space cross times space 3 over denominator 4 end fraction space equals space 27 space space space therefore space space space straight r space equals space cube root of 27 space equals space 3 space cm$

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Mensuration - Volume and Surface Areas

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Three spherical balls of radii 1 cm, 2 cm and 3 cm are melted to form a single spherical ball. In the process, the loss of material is 25%. The radius of the new ball is 6 cm 5 cm 3 cm 3 cm

Mensuration - Volume and Surface Areas

QA01

Three spherical balls of radii 1 cm, 2 cm and 3 cm are melted to form a single spherical ball. In the process, the loss of material is 25%. The radius of the new ball is

6 cm

5 cm

3 cm

3 cm