Question #20ea7

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Answer 1 · 2018-01-09T04:29:04

#color(red)(r = 7 cm, h = 14 cm)#

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#C S A = A_c = 2 pi r h#

#T S A = A_t = 2 pi r h + 2 pi r^2#

#A_t = 924 cm^2#

Given #C S A : T S A = 2 : 3#

#:. A_c = 2 pi r h = (2/3) * 924 = 616 cm^2#

#A_t - A_c = 924 - 616 = 308#

Also, #A_t - A_c = (2 pi r h + 2 pi r^2) - ( 2 pi r h) = 2 pi r^2#

Hence #2 pi r^2 = 308#

#r = sqrt(308/(2pi)) = sqrt(49) = 7 cm#

We know, #A_c = 2 pi r h = 616#

#h = 616 / (2 * pi * 7) = 616 / 44 = 14 cm#

#color(red)(r = 7 cm, h = 14 cm)#