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  cos A = r:R sin A = v:R V2 =  6π v    (3r2 +v2)  V = V1+V2 =21   34 π R3 = 32 π R3  V2 =  6π R sin A    (3(R cos A)2 +(R sin A)2)  V2 =  6π R3 sin A    (3(cos A)2 +(sin A)2)   32 π R3 = V1 +  6π R3 sin A    (3(cos A)2 +(sin A)2)  k=6π sin(A) (3 (cos(A))2+(sin(A))2)=63.1416 sin0.5236 (3 (cos0.5236)2+(sin0.5236)2)0.6545   32 π R3 = 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 cos0.523616.5229 cm v=R sin(A)=19.079 sin0.52369.5395 cm V2=6π v (3 r2+v2)=63.1416 9.5395 (3 16.52292+9.53952)=11500004545.4545 cm3  V8=VV2=111600001150000=1116000050000=11110000=10000 cm3 V8 = V1  R=19.079=19.079 cm

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