A metallic sphere of radius 6 , cm is melted | vedclass

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Question

(A) The volume of the metallic sphere is given by $V = \frac{4}{3} \pi r^3$,where $r = 6 \, cm$.$V = \frac{4}{3} 	imes \pi 	imes (6)^3 = \frac{4}{3}

Vedclass · Accepted Answer

$11.52$

Vedclass · Answer

(A) The volume of the metallic sphere is given by $V = \frac{4}{3} \pi r^3$,where $r = 6 \, cm$.$V = \frac{4}{3} 	imes \pi 	imes (6)^3 = \frac{4}{3} 	imes \pi 	imes 216 = 288 \pi \, cm^3$.The wire is in the shape of a cylinder with diameter $1 \, cm$,so the radius $R = 0.5 \, cm = \frac{1}{2} \, cm$.Let the length of the wire be $h$. The volume of the wire is $V = \pi R^2 h$.Equating the volumes: $288 \pi = \pi 	imes (\frac{1}{2})^2 	imes h$.$288 = \frac{1}{4} 	imes h$.$h = 288 	imes 4 = 1152 \, cm$.Since $100 \, cm = 1 \, m$,the length in metres is $1152 / 100 = 11.52 \, m$.

Part $I$	Part $II$
$1.$ Volume of a cuboid	$a.$ $\frac{1}{3} \pi r^{2} h$
$2.$ Volume of a cone	$b.$ $\pi r^{2} h$
$3.$ Volume of a cylinder	$c.$ $\frac{4}{3} \pi r^{3}$
$4.$ Volume of a sphere	$d.$ $lbh$

$A$ metallic sphere of radius $6 \, cm$ is melted and recast into a wire with diameter $1 \, cm$. Find the length of the wire in metres.

Similar Questions

$A$ sphere and a solid hemisphere have equal radii. Then,the ratio of the surface area of the sphere and $TSA$ of the hemisphere is $\ldots \ldots \ldots \ldots$

$CSA$ of a hemisphere with diameter $20 \, cm$ is $\ldots \ldots \ldots cm^{2}$. (in $\pi$)

Total Surface Area of a cone $= \dots$

Curved surface area of a cone = ....................

Which of the following correctly matches the information given in Part $I$ and Part $II$?

Part $I$ Part $II$

$1.$ Volume of a cuboid $a.$ $\frac{1}{3} \pi r^{2} h$

$2.$ Volume of a cone $b.$ $\pi r^{2} h$

$3.$ Volume of a cylinder $c.$ $\frac{4}{3} \pi r^{3}$

$4.$ Volume of a sphere $d.$ $lbh$

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