(B) 14cm
Volume of circular shell = Volume of cone recast by liquefying
For Spherical Shell,
Inside measurement, d1 = 4 cm
Inside range, r1 = 2 cm
[ as range = 1/2 diameter]
Outer measurement, d2 = 8 cm
Outer range, r2 = 4 cm
Presently,
As volume of circular shell
![\[=\text{ }4/3\text{ }\pi \text{ }\left( r23\text{ }\text{ }r13 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1847d3e57c0361151dd3e5d75000d165_l3.png "Rendered by QuickLaTeX.com")
where r1 and r2 are inside and outside radii individually.
volume of given shell
![\[=\text{ }4/3\text{ }\pi \text{ }\left( 43\text{ }\text{ }23 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-36d58097cc40d000cd2c006819b47ebe_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }4/3\text{ }\pi \text{ }\left( 56 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-567599f63325a76b5e417862da375951_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left( 224/3 \right)\text{ }\pi \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c0edb6bf6ac52f6cc690b9d997503128_l3.png "Rendered by QuickLaTeX.com")
We realize that,
Volume of cone = 224π/3 cm3
For cone,
Base width = 8 cm
Base range, r = 4 cm
Let Height of cone = ‘h’.
We know,
Volume of cone
![\[=\text{ }\left( 1/3 \right)\text{ }\pi \text{ }r2h,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0f5bb308e3b7e1129de1cce7ed36b01e_l3.png "Rendered by QuickLaTeX.com")
Where r = Base range and h = tallness of cone
Volume of given cone
![\[=\text{ }\left( 1/3 \right)\text{ }\pi \text{ }42h\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-72a66ade99926ecd6d34c42b0909454b_l3.png "Rendered by QuickLaTeX.com")
![\[\Rightarrow 224\pi /3\text{ }=\text{ }16\pi h/3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ec9dd8ace7dfae7e8999adff75b187ba_l3.png "Rendered by QuickLaTeX.com")
![\[\Rightarrow 16h\text{ }=\text{ }224\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b5bfedb03a13e813b5acfc86fe68bb40_l3.png "Rendered by QuickLaTeX.com")
h = 14 cm
Along these lines, Height of cone is 14 cm.