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Question

(B) Given,internal diameter of the spherical shell $= 4 \, cm$ and external diameter $= 8 \, cm$.Internal radius of the spherical shell,$r_1 = \frac{4

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(B) Given,internal diameter of the spherical shell $= 4 \, cm$ and external diameter $= 8 \, cm$.Internal radius of the spherical shell,$r_1 = \frac{4}{2} = 2 \, cm$.External radius of the spherical shell,$r_2 = \frac{8}{2} = 4 \, cm$.Volume of the spherical shell $= \frac{4}{3} \pi (r_2^3 - r_1^3) = \frac{4}{3} \pi (4^3 - 2^3) = \frac{4}{3} \pi (64 - 8) = \frac{4}{3} \pi (56) = \frac{224}{3} \pi \, cm^3$.Let the height of the cone be $h \, cm$ and the radius of the base be $R = \frac{8}{2} = 4 \, cm$.Since the shell is recast into a cone,their volumes are equal:Volume of cone $= \frac{1}{3} \pi R^2 h = \frac{1}{3} \pi (4)^2 h = \frac{16}{3} \pi h$.Equating the volumes: $\frac{16}{3} \pi h = \frac{224}{3} \pi$.$16h = 224$.$h = \frac{224}{16} = 14 \, cm$.Thus,the height of the cone is $14 \, cm$.

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 spherical shell of internal and external diameters $4 \, cm$ and $8 \, cm$,respectively,is melted and recast into the form of a cone of base diameter $8 \, cm$. The height of the cone is (in $cm$):

Similar Questions

$A$ metallic sphere with radius $18 \,cm$ is melted and recast to produce cylinders with radius $3 \,cm$ and height $12 \,cm$. Find the number of cylinders produced.

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 $d.$ $lbh$

The radius and height of a cone are both $3 \, cm$. Then,its volume is $\ldots \ldots \ldots \, cm^{3}$. (in $\pi$)

Volume of a cone $= \dots$

The ratio of the radii of two spheres is $3:4$. Then,the ratio of their volumes is $\ldots \ldots \ldots$

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