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

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

$V_1:V_2::64:27$

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

$V_1=64xx4=256$