Question 1043151
First goal is find the volume of each tier.
Second goal is sum the three volumes.
Third goal is find needed volume of raw batter.


BOTTOM
volume is {{{15*pi*(22.5)^2}}} cubic cm's.


MIDDLE
You need to find the square side length of an edge.
A diagonal of square side of the prism is diameter of the bottom tier.
If this diagonal is understood to be cutting two right isosceles from the square lower side or top side, then  for side s,
{{{2s^2=45^2}}}
{{{s^2=45^2/2}}}
{{{s=45/sqrt(2)}}}
{{{s=45sqrt(2)/2}}}
and volume of this tier is {{{s^3}}};---------- ** (No.  See below.)
or
{{{(45/2)^3*sqrt(2)(sqrt(2))^2}}}
{{{(45*45*45*sqrt(2)*2)/(2*4)}}}
{{{45^3*sqrt(2)/4}}}   ---------------------**  (see below)
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Correcting this middle tier volume right now.
Volume here will be {{{15*s*s}}}, because each tier is given 15 cm tall.
This volume,{{{15*(45sqrt(2)/2)^2=15*45^2*2/4=highlight_green((15*45^2)/2)}}}.




TOP TIER
A cylinder, with diameter being same as edge length of the tier below it.
This edge length found was {{{s=45sqrt(2)/2}}}.
Volume, {{{15*pi*(s/2)^2}}}, because we can use RADIUS instead of the full diameter...
{{{15pi*(45sqrt(2)/2)^2}}}----*
{{{15*45^2*pi*2/4}}}
{{{15*45^2*pi/2}}}
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Correcting this part...
Diameter {{{s=45sqrt(2)/2}}}
RADIUS {{{s/2=(45sqrt(2)/2)/2}}}
RADIUS, {{{(45/4)sqrt(2)}}}
Now find this top tier volume.   Cylinder.
{{{15*pi((45/4)sqrt(2))^2}}}
{{{((15*pi*45^2)/4^2)*2}}}
{{{highlight_green(pi(15*45^2)/2^3)}}}


FINAL CAKE VOLUME
sum of the finished three tiers, cubic centimeters
{{{highlight_green(15*pi*(22.5)^2+45^3*sqrt(2)/4+15*45^2*pi/2)}}}-----(No. Still Wrong.  Not yet corrected)
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.
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but this is not finished solving.  This is how much CAKE, but not yet how much batter.  Still is needed, simplification, and then using the ratio for volumes of batter to cake of {{{250/625}}}, and any other computations to finish with a final value answer.


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*  This appears to be a mistake.   The correct expression before computation should be somewhat different...
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** Another mistake found.  Forgot, each tier is 15 cm tall.  This tier is not simply {{{s^3}}}.
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Corrections are now shown for tier middle and tier top, but corrections not yet made for CAKE VOLUME.