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(D) The volume of the solid sphere is given by $V = \frac{4}{3} \pi r^3$. Given $r = 1 \, cm$,the volume is $V = \frac{4}{3} \pi (1)^3 = \frac{4}{3} \

Vedclass · Accepted Answer

$0.11$

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(D) The volume of the solid sphere is given by $V = \frac{4}{3} \pi r^3$. Given $r = 1 \, cm$,the volume is $V = \frac{4}{3} \pi (1)^3 = \frac{4}{3} \pi \, cm^3$.The wire is in the shape of a cylinder. The volume of a cylinder is $V = \pi r_w^2 h$,where $r_w$ is the radius of the wire and $h$ is the length of the wire.Given $h = 100 \, cm$,the volume of the wire is $V = \pi r_w^2 (100) = 100 \pi r_w^2 \, cm^3$.Since the sphere is melted to form the wire,their volumes must be equal:$100 \pi r_w^2 = \frac{4}{3} \pi$Dividing both sides by $\pi$:$100 r_w^2 = \frac{4}{3}$$r_w^2 = \frac{4}{300} = \frac{1}{75}$$r_w = \sqrt{\frac{1}{75}} = \frac{1}{\sqrt{25 	imes 3}} = \frac{1}{5 \sqrt{3}}$Using $\sqrt{3} = 1.732$:$r_w = \frac{1}{5 	imes 1.732} = \frac{1}{8.66} \approx 0.115 \, cm$.Rounding to two decimal places,the radius is approximately $0.11 \, cm$.

$A$ solid sphere of radius $1 \, cm$ is melted to convert into a wire of length $100 \, cm$. The radius of the wire (using $\sqrt{3} = 1.732$) is ......... $cm$.

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