CSA of cone = 550 cm^2 , height = 24 cm. find volume = ??

1.	CSA of cone = 550 cm^2 , height = 24 cm. find volume = ??
Answer» Height of the cone = 24 cmLet radius be r cm and slant height be l cm.{tex}\\therefore \\quad l = \\sqrt { h ^ { 2 } + r ^ { 2 } } \\Rightarrow l = \\sqrt { 24 ^ { 2 } + r ^ { 2 } }{/tex}{tex}\\Rightarrow \\quad l = \\sqrt { 576 + r ^ { 2 } } {/tex}Now, curved surface area = 550 cm2{tex}\\Rightarrow \\quad \\pi r l = 550{/tex}{tex}\\Rightarrow \\quad \\frac { 22 } { 7 } \\times r \\times \\sqrt { 576 + r ^ { 2 } } = 550{/tex}{tex}\\Rightarrow \\quad r \\times \\sqrt { 576 + r ^ { 2 } } = 175{/tex}On squaring both sides, we getr2(576 + r2) = 30625{tex}\\Rightarrow{/tex}\xa0r4\xa0+ 576r2\xa0- 30625 = 0{tex}\\Rightarrow{/tex}\xa0r4\xa0+ 625r2\xa0- 49r2\xa0- 30625 = 0{tex}\\Rightarrow{/tex}\xa0r2(r2\xa0+ 625) - 49(r2\xa0+ 625) = 0{tex}\\Rightarrow{/tex}\xa0(r2\xa0+ 625)(r2\xa0-\xa049) =0{tex}\\Rightarrow{/tex}\xa0r2\xa0= -625 or r2\xa0= 49rejecting r2\xa0= -625we get, r2\xa0= 49{tex}\\Rightarrow r = 7 \\mathrm { cm }{/tex}Now, volume =\xa0{tex}\\frac { 1 } { 3 } \\pi r ^ { 2 } h{/tex}{tex}= \\frac { 1 } { 3 } \\times \\frac { 22 } { 7 } \\times 7 \\times 7 \\times 24{/tex}= 1232 cm3

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