A metallic sphere of radius 6.9cm is melted and recast into the shape of a cylinder of radius 10cm. find the height of the cylinder.
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A metallic sphere of radius 6.9cm is melted and recast into the shape of a cylinder of radius 10cm. find the height of the cylinder.
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Answer:
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Step-by-step explanation:
[tex]so \: here \: for \: a \: metallic \: sphere \\ radius(r) = 6.9 \: cm \\ \\ also \: for \: a \: cylinder \\ radius(R) = 10 \: cm \\ so \: let \: the \: height \: of \: cylinder \: be \:h[/tex]
[tex]so \: as \: sphere \: is \: melted \: and \: recasted \: into \: cylinder \\ volume \: of \: metallic \: sphere = volume \: of \: cylinder[/tex]
[tex]so \: we \: know \: that \: \\ volume \: of \: metallic \: sphere = 4 \div 3\pi rcube \\ volume \: of \: cylinder =\pi \: R.square \: h[/tex]
[tex]thus \: then \\ 4 \div 3\pi.r \: cube = \pi.R \: square \: h \\ 4 \div 3 \times (6.9)cube = (10)square.h \\ ie \: 4 \div 3 \times 328.509 = 100h \\ ie \: 4 \times 109.503 = 100h \\ ie \: 438.012 = 100h \\ ie \: h = 438.012 \div 100 \\ \\ so \: h = 4.38012 \\ ie \: h = 4.38 \: cm \: approximately[/tex]