The hemisphere

The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?

Correct result:

R =  19.079 cm

Solution:

A=30 rad=30 π180 =30 3.1415926180 =0.5236=π/6 V1=10 l cm3=10 1000  cm3=10000 cm3  cosA=r:R sinA=v:R V2=πv6 (3r2+v2)  V=V1+V2=12 43πR3=23πR3  V2=πRsinA6 (3(RcosA)2+(RsinA)2)  V2=πR3 sinA6 (3(cosA)2+(sinA)2)  23πR3=V1+πR3 sinA6 (3(cosA)2+(sinA)2)  k=π sin(A)6 (3 (cos(A))2+(sin(A))2)=3.1416 sin(0.5236)6 (3 (cos(0.5236))2+(sin(0.5236))2)0.6545  23πR3=V1+k R3  R=V123 πk3=1000023 3.14160.6545319.079 cm   V=23 π R3=23 3.1416 19.079314545.4545 cm3 r=R cos(A)=19.079 cos(0.5236)16.5229 cm v=R sin(A)=19.079 sin(0.5236)9.5395 cm V2=π v6 (3 r2+v2)=3.1416 9.53956 (3 16.52292+9.53952)=50000114545.4545 cm3  V8=VV2=14545.45454545.4545=10000 cm3 V8=V1   R=19.079=19.079 cm



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