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 answer:

R =  19.079 cm

Step-by-step explanation:

A=30° rad=30° 180π =30° 1803.1415926 =0.5236=π/6 V1=10 l cm3=10 1000  cm3=10000 cm3  cosA=r:R sinA=v:R V2=6πv (3r2+v2)  V=V1+V2=21 34πR3=32πR3  V2=6πRsinA (3(RcosA)2+(RsinA)2)  V2=6πR3 sinA (3(cosA)2+(sinA)2)  32πR3=V1+6πR3 sinA (3(cosA)2+(sinA)2)  k=6π sin(A) (3 (cos(A))2+(sin(A))2)=63.1416 sin(0.5236) (3 (cos(0.5236))2+(sin(0.5236))2)0.6545  32πR3=V1+k R3  R=332 πkV1=332 3.14160.65451000019.079 cm  V=32 π R3=32 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=6π v (3 r2+v2)=63.1416 9.5395 (3 16.52292+9.53952)=11500004545.4545 cm3  V8=VV2=14545.45454545.4545=10000 cm3 V8=V1  R=19.079=19.079 cm



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