A glass cylinder with diameter 20cm has water to a height of 9 cm.A metal cube of 8 cm edge immersed in it completely.Calculate the height by which water will rise in the cylinder.(Take π = 3.142)
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Volume of water in the cylinder = pi*r*r*h = pi*10*10*9 = 2827.8 cm^3
Volume of metal cube = side^3 = (8)^3 = 512 cm^3
Total volume of the water column after insertion of cube = 2827.8 +512 cm^3 = 3339.8 cm^3
This volume = pi*r*r*h
Only the height of the column changes after insertion of cube, radius remains the same. Therefore we substitute the value of r and new volume in this formula,
3339.8 = 3.142*10*10*h
=> h= 10.63 cm
Previous height = 9 cm
Rise = new height - previous height
Rise = 10.63-9 cm = 1.63 cm
Volume of metal cube = side^3 = (8)^3 = 512 cm^3
Total volume of the water column after insertion of cube = 2827.8 +512 cm^3 = 3339.8 cm^3
This volume = pi*r*r*h
Only the height of the column changes after insertion of cube, radius remains the same. Therefore we substitute the value of r and new volume in this formula,
3339.8 = 3.142*10*10*h
=> h= 10.63 cm
Previous height = 9 cm
Rise = new height - previous height
Rise = 10.63-9 cm = 1.63 cm
Answered by
1
Answer:
H = 9 cm
diameter = 20 cm so,radius = 10 cm
side of the cube = 8 cm
Total volume of the cylinder
(after cube is immersed) = Volume of water in cylinder + Volume of water displaced or volume of the cube
= 22/7*10*10*9 + 8*8*8
= 19800/7 + 512
= 2828.57 + 512
= 3340.57 cu cm
Now, height of water, h1 can be found by equating πr²h1 with this volume.
So,
22/7*10*10*h1 = 3340.57
h1 = (3340.57 × 7)/2200
h1 = 23383.99/2200
Height = 10.63 cm
Rise in the water level in the cylinder
= h1 - h
= 10.63 - 9
= 1.63 cm
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