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A cone of height is 20 …

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A cone of height is 20 cm and radius of base 5cm is made up of modelling clay .A child reshapes it in the form of a shpere .Find the diameter of the sphere

    • Posted by Lucky Pant 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Given height of the cone = 20 cm and
    Radius of the cone = 5 cm
    Let the radius of the sphere be R cm.
    Given
    Volume of cone = Volume of sphere
    {tex}\Rightarrow \frac { 1 } { 3 } \pi r ^ { 2 } h = \frac { 4 } { 3 } \pi R ^ { 3 }{/tex}
    {tex}\Rightarrow{/tex} r2h = 4R3
    {tex}\Rightarrow{/tex} {tex}R ^ { 3 } = \frac { 5 \times 5 \times 20 } { 4 }{/tex}
    {tex}\Rightarrow{/tex} R3 = 125
    {tex}\Rightarrow{/tex} R = 5 cm
    {tex}\Rightarrow{/tex} Radius of the sphere is 5 cm.
    {tex}\Rightarrow{/tex} The diameter of the sphere = 5 {tex}\times{/tex} 2 = 10 cm

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