A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?
Answers
Answer:
60 cylindrical bottles are required to empty a hemispherical bowl.
Step-by-step explanation:
SOLUTION:
Given :
Internal radius of the hemispherical bowl , R = 15 cm
Diameter of the cylindrical bottle = 5 cm
Radius of the cylindrical bottle , r = 5/2 cm = 2.5 cm
Height of the cylindrical bottle , h = 6 cm
Number of cylindrical shaped bottles required to empty a hemispherical bowl , n = Volume of hemispherical bowl / Volume of each cylindrical shaped bottles
n = 2/3 × πR³ / πr²h
= 2/3 × 15³ / 2.5² × 6
= 10 × 225 / 6.25 × 6
= 2250/ 37.5 = 22500/375
n = 60
Hence, 60 cylindrical bottles are required to empty a hemispherical bowl.
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Answer:
Step-by-step explanation:
volume of hemisphere = n(volume of cylinder)
volume of hemisphere is 2/3pir^3
volume of cylinder = pir^2h
volume of hemisphere is 2/3pir^3
= 2/3 x 22/7 x 15/2 x 15/2 x 15/2
=11x15x15x5/7x2
=883.9 cm^3
now
volume of cylinder = pir^2h
=n(22/7 x 5/2 x 5/2 x 6)
= n(11/7 x 25 x 3)
=n(117.8)
volume of hemisphere = n(volume of cylinder)
883.9 cm^3 = n(117.8)
n = 883.9 /117.8