A cone of height 24, cm and radius of base 6, | vedclass

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(A) The volume of the cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.Substituting the given values,$r = 6\, cm$ and $h = 24\, cm$:$V = \frac

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$6$

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(A) The volume of the cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.Substituting the given values,$r = 6\, cm$ and $h = 24\, cm$:$V = \frac{1}{3} 	imes \pi 	imes 6^2 	imes 24 = \frac{1}{3} 	imes \pi 	imes 36 	imes 24 = 288\pi\, cm^3$.Let the radius of the sphere be $R$. The volume of the sphere is given by $V = \frac{4}{3} \pi R^3$.Since the volume of the clay remains the same after reshaping,we equate the two volumes:$\frac{4}{3} \pi R^3 = 288\pi$.Dividing both sides by $\pi$ and multiplying by $\frac{3}{4}$:$R^3 = 288 	imes \frac{3}{4} = 72 	imes 3 = 216$.Taking the cube root of both sides:$R = \sqrt[3]{216} = 6\, cm$.Thus,the radius of the sphere is $6\, cm$.

$A$ cone of height $24\, cm$ and radius of base $6\, cm$ is made up of modelling clay. $A$ child reshapes it in the form of a sphere. Find the radius of the sphere (in $cm$).

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