Question #9717d

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Answer 1 · 2017-01-30T13:35:14

#9:16#

For two similar solids

#"(ratio of surface areas)=(ratio of lengths)"^2#

#"(ratio of volumes)=(ratio of lengths)"^3#

#"to tackle this problem we go from"#
#"the volume ratio , to length ratio then to area ratio"#

let the ratio of lengths be #" "l_1:l_2"#

#"where "l_1 < l_2#

#"ratio of volumes"::(27:64)#

#:.l_1 :l_2::root(3)(27:64)#

#=>l_1 :l_2::3:4#

#" ratio of surface areas ="(l_1:l_2)^2"#

#"ratio of surface areas"::(3:4)^2::9:16#