Answer:
864.
Step-by-step explanation:
1) the required volume can be calculated according to the formula (see also the attachment):
V=Area(BKS)*height;
2) if to see the triangle ABC (see the attachment), then m∠C=90°; m∠A=30° and m∠B=60°;
3) the length of AC=BC*cot(m∠A)=2√3*√3=6 [cm];
4) if AC=6 [cm], then BS=36-2*BC=24 [cm];
5) in the equilateral triangle BKS BS=BK=KS=24 [cm], then the Area(BKS)=BS²√3/4=144√3 [cm²];
6) if the height is 2√3 [cm] and Area(BKS)=144√3 [cm²], then
V=144√3*2√3=864 [cm³].
