Question

Agulab jamun, contains sugar syrup up to about 50% of its volume. Find approximately how much syrup would be found in 10 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 10 cm and diameter 1.8 cm.​

Answer 1

Answer:

  h=5cm

length  of the  cylinder h=5−2.8=2.2

volume of gulab jamun=volume of cylinder+volume of 2 

hemispheres.

volume=3πr2h+34πr3

             =722×1.4×1.43(3×2.2+4×1.4)

            =36.16(12.2)

           =375.152=25.05cm cube.

 jamuns=45

 Hence there are 45 gulab jamuns 

 volume=45×25.05=1127.2830 percentage of syrup.

  volume =1127.28×10030=338.184cmcube

Answer 2

Given - Radius and length of cylinder

Find - Volume of syrup in 10 gulab jamun

Solution - Sugar syrup to be found in 10 gulab jamuns is 297 cm³.

The volume of cylinder with two hemispherical ends can be calculated by the formula -

$\pi {r}^{2} h + 2 (\frac{2\pi {r}^{3} }{3} )$

So, volume of cylinder =

$\pi {r}^{2} (h + \frac{4r}{3} )$

Keeping the values in formula to find the volume of cylinder.

Volume of cylinder =

$\frac{22}{7} \times {0.9}^{2} (10 + \frac{4 \times 10}{3} )$

Volume of cylinder =

$2.5 \times (10 + \frac{40}{3} )$

Volume of cylinder =

$2.5 \times \frac{70}{3}$

Volume of cylinder = 59.4 cm³

Thus, volume of one gulab jamun is 59.4 cm³.

Sugar syrup absorbed is 50% of volume.

So, sugar syrup absorbed = 59.4*50/100

Sugar syrup = 29.7 cm³

Sugar syrup absorbed by 1 gulab jamun = 29.7 cm³.

Sugar syrup absorbed by 10 gulab jamun = 29.7*10

Sugar syrup absorbed by 10 gulab jamun = 297 cm³.