If three diametrical cuts perpendicular to each other are made on a painted metal sphere, what would be the ratio of the unpainted surface to the painted surface?
Answers
Given : three diametrical cuts perpendicular to each other are made on a painted metal sphere,
To Find : what would be the ratio of the unpainted surface to the painted surface?
Step-by-step explanation:
three diametrical cuts perpendicular to each other are made on a painted metal sphere,
Hence it will cut in 8 Equal pieces
Surface Area of each painted face = (1/8) 4πr²
= (1/2) πr²
Each Piece will have The three plane surfaces which are 1 quadrant ( 1/4 ) of a circle which will not be painted
Area = 3 ( 1/4) π r²
= (3/4) π r²
painted face Surface Area of each piece = (1/2) πr²
unpainted surface Area of each piece = (3/4) π r²
ratio of the unpainted surface to the painted surface = (3/4) π r² / (1/2) πr²
= 3/2
= 3 : 2
ratio of the unpainted surface to the painted surface = 3 : 2
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