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The volume of right circular cone is 9856cm³.If the radius of base 14 cm.find the----->1. height of cone2.Slant height​

Answer» <html><body><p><img align="absmiddle" alt="\underline{\underline{\sf{\maltese\:\:Question}}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Cunderline%7B%5Csf%7B%5Cmaltese%5C%3A%5C%3AQuestion%7D%7D%7D" title="\underline{\underline{\sf{\maltese\:\:Question}}}"/></p><p> </p><p> </p><p> </p><p></p><h3>The volume of right circular cone is 9856 cm³. If the radius of base 14 cm. Find the :</h3><p></p><p>Height of Cone</p><p>Slant Height</p><p><img align="absmiddle" alt="\underline{\underline{\sf{\maltese\:\:Given}}}" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Cunderline%7B%5Csf%7B%5Cmaltese%5C%3A%5C%3AGiven%7D%7D%7D" title="\underline{\underline{\sf{\maltese\:\:Given}}}"/></p><p> </p><p> </p><p> </p><p></p><p>The volume of right circular cone = 9856 cm³</p><p>Radius of Base = 14 cm</p><p><img align="absmiddle" alt="\underline{\underline{\sf{\maltese\:\:To\:Find}}}" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Cunderline%7B%5Csf%7B%5Cmaltese%5C%3A%5C%3ATo%5C%3AFind%7D%7D%7D" title="\underline{\underline{\sf{\maltese\:\:To\:Find}}}"/></p><p> </p><p> </p><p> </p><p> </p><p></p><p>Height of Cone</p><p>Slant Height</p><p><img align="absmiddle" alt="\underline{\underline{\sf{\maltese\:\:Answer}}}" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Cunderline%7B%5Csf%7B%5Cmaltese%5C%3A%5C%3AAnswer%7D%7D%7D" title="\underline{\underline{\sf{\maltese\:\:Answer}}}"/> </p><p> </p><p> </p><p> </p><p></p><p>Height of Cone = 48 cm</p><p>Slant Height of Cone = 50 cm</p><p><img align="absmiddle" alt="\underline{\underline{\sf{\maltese\:\:Calculations}}}" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Cunderline%7B%5Csf%7B%5Cmaltese%5C%3A%5C%3ACalculations%7D%7D%7D" title="\underline{\underline{\sf{\maltese\:\:Calculations}}}"/> </p><p></p><p> </p><p> </p><p> </p><p> </p><p></p><h3>♣ First Let's Find Height of Cone</h3><p></p><p>Volume of Right Circular Cone = 9856 cm³</p><p></p><p>⇒ 1/3πr²h = 9856 cm³</p><p></p><p>⇒ 1/3 × π × r² × h = 9856 cm³</p><p></p><p>⇒ 1/3 × 22/7 × r² × h = 9856 cm³ (∵ π = 22/7)</p><p></p><p>⇒ 22 × 1/7 × 3 × r² × h = 9856 cm³</p><p></p><p>⇒ 22/21 × r² × h = 9856 cm³</p><p></p><p>⇒ 22/21 × r² × h = 9856 cm³ (Given r = 14 cm)</p><p></p><p>⇒ 22/21 × (14 cm)² × h = 9856 cm³ </p><p></p><p>⇒ 22/21 × <a href="https://interviewquestions.tuteehub.com/tag/196-281839" style="font-weight:bold;" target="_blank" title="Click to know more about 196">196</a> cm² × h = 9856 cm³ </p><p></p><p>⇒ (22 × 196)/21 cm² × h = 9856 cm³ </p><p></p><p>⇒ 4312/21 cm² × h = 9856 cm³ </p><p></p><p>⇒ 616/3 cm² × h = 9856 cm³ </p><p></p><h3>Multiplying both sides by 3</h3><p></p><p>⇒ 3 × (616/3) cm² × h = 3 × 9856 cm³ </p><p></p><p>⇒ 616 cm² × h = 29568 cm³ </p><p></p><h3>Dividing both sides by 616 cm²</h3><p></p><p>⇒ (616 cm² × h)/616 cm² = 29568 cm³/616 cm²</p><p></p><p>⇒ h = 29568/616 cm</p><p></p><p>⇒ h = 48 cm</p><p></p><p>∴ Height of Cone = 48 cm</p><p></p><p></p><p>_______________________________________</p><p></p><h3>♣ Now Let's Find Slant Height</h3><p></p><p>Slant Height = √(r² + h²)</p><p></p><p>⇒ Slant Height = √[(14 cm)² + h²] (Given r = 14 cm)</p><p></p><p>⇒ Slant Height = √[196 cm² + h²] </p><p></p><p>⇒ Slant Height = √[196 cm² + (48 cm)²] (We <a href="https://interviewquestions.tuteehub.com/tag/found-458144" style="font-weight:bold;" target="_blank" title="Click to know more about FOUND">FOUND</a> : h = 48 cm)</p><p></p><p>⇒ Slant Height = √[196 cm² + 2304 cm²]</p><p></p><p>⇒ Slant Height = √[2500 cm²]</p><p></p><p>⇒ Slant Height = √[50² cm²]</p><p></p><p>⇒ Slant Height = √[50²] cm</p><p></p><p>⇒ Slant Height = 50 cm</p><p></p><p>∴ Slant Height of Cone = 50 cm</p><p></p><p>___________________________</p><p></p><h3>Request :</h3><p></p><p>If there is any difficulty viewing this answer in <a href="https://interviewquestions.tuteehub.com/tag/app-25615" style="font-weight:bold;" target="_blank" title="Click to know more about APP">APP</a>, Kindly see this answer at Web (https://brainly.in/) for <a href="https://interviewquestions.tuteehub.com/tag/clear-408920" style="font-weight:bold;" target="_blank" title="Click to know more about CLEAR">CLEAR</a> steps and understanding.</p></body></html>


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