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A cone of height 24 cm …

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A cone of height 24 cm and radius of base 6cm is made up of modelling clay a child reshapes it in the form of a sphere find the radius of sphere and hence the surface area of this sphere

    • Posted by S Tiwari 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    Radius of the cone, r2 = 6cm

    Height of the cone, h = 24cm

    Let the radius of the sphere be 'r1'

    Volume of the sphere = Volume of the cone

    {tex}\therefore \quad \frac { 4 } { 3 } \pi r _ { 1 } ^ { 3 } = \frac { 1 } { 3 } \pi r _ { 2 } ^ { 2 } h{/tex}

    {tex}\frac { 4 } { 3 } \times r _ { 1 } ^ { 3 } = ( 6 ) ^ { 2 } \times \frac { 24 } { 3 }{/tex}

    {tex}4 r _ { 1 } ^ { 3 } = 36 \times 24{/tex}

    {tex}r _ { 1 } ^ { 3 } = 6 ^ { 3 }{/tex}

    {tex}r _ { 1 } = 6{/tex}

    Hence, radius of the sphere = 6 cm.

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