If the circumference of the circular base of a cylinder is doubled, how does the volume of the cylinder change? A) The volume doubled. B) The volume tripled. C) The volume quadrupled. D) The volume is eight times larger.

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christophershap78g4u christophershap78g4u

15-04-2018
Mathematics

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If the circumference of the circular base of a cylinder is doubled, how does the volume of the cylinder change? A) The volume doubled. B) The volume tripled. C) The volume quadrupled. D) The volume is eight times larger.

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1rstar 1rstar · Answer 1 · 2018-04-15T17:54:35+02:00

[tex]VOLUMES \\ \\ \\ As \: we \: know \: , \: \: \\ \\ Volume \: of \: cylinder \: = \pi {r}^{2} h \\ \\ Where \: ,\\ \\ r \: is \: the \: radius \: W
while \\ h \: is \: the \: height \: of \: the \: cylinder \\ \\ Circumference \: of \: base \: = \: 2 \times \pi \times r \\ \\ As \: 2 \: and \: pi \: are \: constant \: , \: Circumference \: can \: only \\ change \: when \: r \: is \: changed \\ \\ As \: circumference \: got \: doubled \: \\ means \: radius \: got \: twice \\ \\ New \: volume \: = \: \pi {(2r)}^{2} h = 4\pi {r}^{2} h \\ \\ \\ Hence \: , \: the \: volume \: got \: \\ quadrupled \: or \: 4 \: times \: more[/tex]