Question 1025615
*[illustration xc1.png].
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From the illustration,
{{{6+A+5=15}}}
{{{A=4}}}
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{{{5+C+4=15}}}
{{{C=6}}}
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Let's define {{{alpha}}} as the angle whose tangent is equal to,
{{{tan(alpha)=B/A)}}}
You also know that,
{{{cos(alpha)=A/11}}}
{{{cos(alpha)=4/11}}}
{{{alpha=68.7}}}
So then,
{{{B=11sin(68.7)}}}
{{{B=10.25}}}
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Let's define {{{beta}}} as the angle whose tangent is equal to,
{{{tan(beta)=D/C}}}
You also know, 
{{{cos(beta)=C/9}}}
{{{cos(beta)=6/9}}}
{{{beta=48.2}}}
So then similarly,
{{{D=9sin(48.2)}}}
{{{D=6.71}}}
So know we can calculate the depth (as shown by the red line).
{{{D=6+B+D+4}}}
{{{D=6+10.25+6.71+4}}}
{{{D=26.96}}}
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So now the entire volume is made up of water and spheres and is equal to,
{{{V=pi*(15/2)^2*26.96}}}
{{{V=4764.22}}}{{{in^3}}}
{{{V[s1]+V[s2]+V[s3]+V[w]=4764.22}}}
{{{(4/3)pi(r[1]^3+r[2]^3+r[3]^3)+V[w]=4764.22}}}
{{{(4/3)pi(4^3+5^3+6^3)+V[w]=4764.22}}}
{{{1696.46+V[w]=4764.22}}}
{{{highlight_green(V[w]=3067.8)}}}{{{in^3}}}