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Question
A cylindrical can of internal diameter 21 cm contains water . A solid sphere whose diameter is 10.5 cm is lowered into the cylindrical can. The sphere is completely immersed in water . Calculate the rise in water level, assuming that no water overflows.
A cylindrical can of internal diameter 21 cm contains water . A solid sphere whose diameter is 10.5 cm is lowered into the cylindrical can. The sphere is completely immersed in water . Calculate the rise in water level, assuming that no water overflows.
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Solution
SPHERE
Diameter = 10.5 cm.
Radius = 105/20
Volume = 4/3 π r³
4/3 × 22/7 × 105/20×105/20×105/20
= 11×105×105/10×20 cu.cm.
CYLINDER
Diameter = 21cm.
Radius = 21/2 cm.
Volume = πr²h
22/7× 21/2×21/2×h cu.cm
Volume of the cylinder= Volume of the sphere
22/7×21/2×21/2×h = 11×105×105/10×20
11×3/2×21×h = 11×105×105/10×20
h = 11×105×105×2/10×20×3×11×21
h= 1.75
Diameter = 10.5 cm.
Radius = 105/20
Volume = 4/3 π r³
4/3 × 22/7 × 105/20×105/20×105/20
= 11×105×105/10×20 cu.cm.
CYLINDER
Diameter = 21cm.
Radius = 21/2 cm.
Volume = πr²h
22/7× 21/2×21/2×h cu.cm
Volume of the cylinder= Volume of the sphere
22/7×21/2×21/2×h = 11×105×105/10×20
11×3/2×21×h = 11×105×105/10×20
h = 11×105×105×2/10×20×3×11×21
h= 1.75
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