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Q.

About 30% of the volume of a gulab jamun is made up of sugar syrup. Find the approximate amount of syrup contained in 45 gulab jamuns, each measuring 5 cm in length and 2.8 cm in diameter. They are fashioned like cylinders with two hemispherical ends. Use π= 22 7  .


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a

338c m 3  

b

340c m 3  

c

342c m 3  

d

344c m 3    

answer is A.

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Detailed Solution


Given that each Gulab jamun has a cylinder-like shape with two 5-cm hemispherical ends.
Diameter = 2.8cm and sugar syrup makes up about 30% of the volume of each gulab jamun.
A gulab jamun, contains sugar syrup upto about 30% of its volume. Find approximately how much syrup - Sarthaks eConnect | Largest Online Education CommunityDiameter of hemisphere = diameter of cylindrical part
Radius of cylindrical part = radius of hemispherical part
Volume of 1 Gulab jamun = volume of cylindrical part + volume of the 2 hemispherical parts
Volume of cylinder with radius r and height h is given by π r 2 h  .
Volume of hemisphere with radius r is given by 2 3 π r 3  .
Diameter of the Gulab jamun, d = 2.8cm
Radius of cylindrical part = radius of hemispherical part
Radius=r  
Radius=2.8/2  
Radius=1.4cm  
Length of cylindrical part, h
Length=5cm×1.4cm Length=2.2cm  
Put the values of r and h:
⇒Volume=2× 2 3 π r 3 +π r 2 h  
⇒Volume=π r 2 4r 3 +h  
Volume= 22 7 ×1.4×1.4× 4 3 ×1.4+2.2 c m 3  
⇒Volume= 22 7 ×1.4×1.4× 122.2 3 c m 3  
⇒Volume= 75.152 3 c m 3  
Volume of 45 Gulab jamuns = 45 ×  volume of 1 Gulab jamun
⇒Volume=45× 75.152 3 c m 3  
⇒Volume=15×75.152c m 3  
⇒Volume=1127.28c m 3  
Volume of sugar syrup in 45 Gulab jamuns = 30% of volume of 45 Gulab jamun
⇒Volume= 30 100 ×1127.28c m 3  
⇒Volume=338.184c m 3    ⇒Volume=338c m 3 approximately  
Hence, volume of sugar syrup in 45 Gulab jamuns =338c m 3  
Therefore the answer is option (1).
 
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