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?

Question

865 views around the world

You can reuse this answer
Creative Commons License

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#