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Question

(D) The volume of one spherical ball is $V = \frac{4}{3} \pi r^3$,where $r = 3 	ext{ cm}$.Total volume of $10$ balls $= 10 	imes \frac{4}{3} \pi (3)

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$6$

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(D) The volume of one spherical ball is $V = \frac{4}{3} \pi r^3$,where $r = 3 	ext{ cm}$.Total volume of $10$ balls $= 10 	imes \frac{4}{3} \pi (3)^3 = 10 	imes \frac{4}{3} \pi (27) = 360 \pi 	ext{ cm}^3$.Since $20 \%$ of the material is wasted,the volume of the new sphere $V_{new}$ is $80 \%$ of the total initial volume.$V_{new} = 0.80 	imes 360 \pi = 288 \pi 	ext{ cm}^3$.Let the radius of the new sphere be $R$. Then,$\frac{4}{3} \pi R^3 = 288 \pi$.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,$R = \sqrt[3]{216} = 6 	ext{ cm}$.

$10$ identical solid spherical balls of radius $3 \text{ cm}$ are melted to form a single sphere. In this process,$20 \%$ of the solid is wasted. What is the radius (in $\text{cm}$) of the resulting sphere?

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