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The radius and height of a …

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The radius and height of a solid right circular cone are in the ratio 5:12.if its volume is314 cm3 find its tsa

    • Posted by Avaneesh Sharma Mdjssv 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    Let the ratio be x
    {tex}\therefore{/tex} Radius 'r' = 5x
    Height 'h' = 12x
    {tex}\therefore{/tex} Slant height = {tex}\sqrt { r ^ { 2 } + h ^ { 2 } } = \sqrt { ( 5 x ) ^ { 2 } + ( 12 x ) ^ { 2 } }{/tex} =13x
    Now, volume = 314 m3 [given]
    {tex}\Rightarrow {/tex} {tex}\frac { 1 } { 3 } \pi r ^ { 2 } h{/tex} = 314
    {tex}\Rightarrow {/tex} {tex}\frac { 1 } { 3 }{/tex} {tex}\times{/tex} 3.14 {tex}\times{/tex} 25 x2 {tex}\times{/tex} 12x = 314
    {tex}\Rightarrow {/tex} x3 = {tex}\frac { 314 \times 3 } { 3.14 \times 25 \times 12 }{/tex}
    {tex}\Rightarrow {/tex} x = 1
    {tex}\therefore{/tex} Slant height = 13x = 13m
    Radius = 5x = 5m

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