Two similar glasses have diameters of 6 cm and 8 cm respectively. The smaller glass holds 108 milliliters. How do you find the capacity of the larger glass?

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Answer 1 · 2017-11-19T14:15:30

#256# mililiters

#v_1 = pi (d_1/2)^2 h_1#
#v_2=pi(d_2/2)^2 h_2#

but they are similar or

#d_2 = lambda d_1# and
#h_2 = lambda h_1#

then

#v_2 = pi(lambda d_1/2)^2 lambda d_1 = lambda^3 pi(d_1/2)^2 h_1 = lambda^3 v_1#

here #d_1 = 6# and #d_2 = 8# then #lambda = 8/6 = 4/3#

now if #v_1 = 108# then #v_2 = (4/3)^3 108 = 256# mililiters

Answer 2 · 2017-11-20T08:41:12

#256millilitres#

another approach

we can use the relation

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

we have

ratio of lengths

#l_1>l_2#

#l_1:l_2::8:6#

#l_1:l_2::4:3#

ratio of vols

#V_1:v_2=(4:3)^3#

#V_1:V_2::64:27#

#:.V_1=64/cancel(27)xxcancel(108)^4#

#V_1=64xx4=256#