Question

A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see the given figure). [Use = 22 7 ]​

Answer 1

Answer:

Step-by-step explanation:

Total volume of gulabjamun =πr  

2

h+2×  

3

2

​

πr  

3

 

Total volume of 45 gulabjamuns  

V.of cyl= πr  

2

h

V. of hemisphere =  

3

2

​

πr  

3

 

=45× volume of 1 gulabjamun

=45×(πr  

2

h+  

3

4

​

πr  

3

)=45×(π(  

2

d

​

)  

2

h+  

3

4

​

π(  

2

d

​

)  

3

)

=45×π((1.4)  

2

×5+  

3

4

​

(1.4)  

3

)=1902.67cm  

3

 

A gulabjamun syrup percentage =30% of its volume

Total syrup =30% ot total volume =  

100

30

​

×1902.67

                                                          =570.80 cm  

2

Answer 2

Answer:

338.184cm cube

Step-by-step explanation:

h=5cm

length of cylinder=5-2.8=2.2cm

vol.of gulab jamun=vol.of cylinder +vol.of 2 hemispheres

volume=3$\pi$$r^{2}$h+$\frac{4}{3}$$\pi r^{3}$

=$\frac{22}{7}$×1.4×1.4$\frac{(3*2.2+4*1.4)}{3}$

=$\frac{6.16(12.2)}{3}$

=$\frac{75.152}{3}$

=25.05cm cube

jamuns=45

volume=45×25.05=1127.2830 percentage of syrup

volume=1127.28×$\frac{30}{100}$=338.184cmcube