a hemispherical bowl of internal radius 9 cm is full of liquid the liquid is to be filled into cylindrical shaped bottles each of radius 1.5cm and height 4cm .How many bottles are needed to empty the bowl.
Answers
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radius of hemisphere = 9cm
volume of hemisphere =2/3 pi r^3
=2/3*9*9*9pi
=486pi
radius of cylindrical shaped bottles =3/2cm
height=4cm
volume of bottles = pi r^2 h
=3/2x 3/2 * 4pi
=9pi
now,
required number of bottles=volume of hemisphere/volume of bottles
=486pi
=54
therefore, 54 bottles are required to fill the empty bowl...
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Answer:
54 cylindrical bottles are necessary to empty a hemispherical bowl.
Step-by-step explanation:
Given :
Internal radius of the hemispherical bowl , R = 9 cm
Diameter of the cylindrical bottle = 3 cm
Radius of the cylindrical bottle , r = 3/2 cm = 1.5 cm
Height of the cylindrical bottle , h = 4 cm
Number of cylindrical shaped bottles required to empty a hemispherical bowl , n = Volume of hemispherical bowl / Volume of each cylindrical shaped bottles
= 2/3 × πR³ / πr²h
= 2/3 × 9³ / 1.5² × 4
= 2/3 × 729 / 2.25 × 4
= 2 × 243 / 2.25 × 4
= 243 / 2.25 × 2
= 243/ 4.5 = 2430/45 = 54
n = 54
Hence, 54 cylindrical bottles are required to empty a hemispherical bowl.
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