Question

A spherical cannonball 28 cm in diameter is melted and cast into a right circular cone mode whose base is 8 centimetre find the height of cone

Answer 1

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$Diameter \: of \: cannon \: ball = 28 cm \\ Radius \: of \: cannon \: ball = 14 cm \\ \: Volume \: of \: cannon \: ball = \frac{4}{3} \pi {r}^{3} = \frac{4}{3} π {14}^{3} \\ Radius \: of \: Cone = \frac{8}{2} cm = 4cm \\ Volume \: of \: Cone \: = \frac{1}{3} π {r}^{2} h = \frac{1}{3} π( { 4 }^{2} ) h \\ Let \: h \: be \: the \: height \: of \: the \: cone. \\ From \: statement: \\ Volume \: of \: cannon \: ball \: = Volume \: of \: Cone \\ ⇨ \frac{4}{3} π {(14)}^{3} = \frac{1}{3} π {(4)}^{2} h \\ h = 686\\ Therefore, \: height \: of \: the \: cone \: is \: 686 cm.$