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A hemispherical tank having a radius "R" contains liquids A and B with a total depth...

A hemispherical tank having a radius "R" contains liquids A and B with a total depth of 12 cm. Liquid B is on top of liquid A. Liquid A has a depth of 8 cm. If the volume of liquids A and B are equal, compute the area of contact between the two liquids and the tank.

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solution À Hemispherical tank of radius p liquid B liquid a depth of liquid A= A = 8 cm total depth of tot liquids = 12R R-127 R-121 Du an 12 82 8 from the diagram X R-12 cms Cms R-8 y = radius 8 = R?- (R-12) 2 24R-144 82 = J R2(R-8)= = √16 R-6Volume of Al Calculated from heighth ao to height h=8cms Volume 8 11&2 dh ra R 7 r= J R²_(R-h) 2 h I 8:11 R² R²+2 Rhuh? 8:5VA TR h²th This ] 64 R-(170.67) TI (64R-170.67) Volume of B is VA VB given by h:12 ve Strech h=8 v BE S h:12 II (2 Rh - h2)Area of contact of liquids AfB is 2 Tr, = 11x (13)? Area of Contat 535-5 cm² Between liquids 535.5 (m2 iis Area of contact BeTotal surface area of Hemisphere a 2те 2 2 T* (14.67) = 1351.5 for Hemisphere solid Angle = π = 180 degre. to calculate solid

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