Question

A gulab-jamun contain 40 % sugar syrup in it. Find how much syrup would be there in 50 gulab-jamuns, each shaped like a cylinder with two hemispherical ends with total length 5 cm and diameter 2.8 cm.

Answer 1

HELLO DEAR,

GIVEN:- height of gulab jamun = 5cm
diameter of hemisphere = 2.8cm
radius of hemisphere = 2.8/2 = 1.4cm = r(radius of cylinder)

Now, height of cylinder = 5 - 1.4 - 1.4 = 2.2cm​

∴ volume of 1 gulab jamun = volume of cylinder + 2(volume of hemisphere)

⇒πr²h + 2(⅔πr³)

⇒πr²{h + 4/3r)​

⇒22/7 * (1.4)² * {2.2 + 4/3*(1.4)}

⇒22/7 * (1.4)² * {6.6 + 5.6}/3

⇒22/7 * (1.4)² *12.2/3

Volume of 50 gulab jamuns
⇒50 *22/7 * (1.4)² * (12.2)/3

∴ volume of syrup
⇒40/100 * 50 * 22/7 * 1.4 * 1.4 * 12.2/3

⇒4/10 * 50 * 22 * 0.2 * 1.4 * 12.2/3

⇒20 * 22 * 0.2 * 1.4 * 12.2/3

⇒88 * 1.4 * 12.2/3

⇒88 * 17.08/3

⇒1503.04/3

⇒501.0133cm³

⇒(501.0133)/100litre [1l = 1000cm3]

⇒0.501013litre.

the volume of syrup in 50gulab jamun is 0.5litre


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Answer:

The Syrup in 50 Gulab Jamuns is 500.6 c$m^{3}$

Step-by-step explanation:

Formula to find the volume of a Cylinder:  

${\boxed{\boxed{\sf{\implies \pi r^{2}h}}}}$

Formula to find the volume of a Hemisphere:

${\boxed{\boxed{\sf{\implies \dfrac{2}{3}\pi r^{3}}}}}$

Height of the cylinder = 5 - 1.4 - 1.4 = 2.2 cm

Radius of Hemisphere = 2.8 / 2 = 1.4 cm (2.8 is the diameter of the hemisphere)

Volume of Cylinder = $\pi$ $r^{2}$h

=> 22 / 7 * 1.4 * 1.4 * 2.2

=> 4.4 * 1.4 * 2.2

=> 13.55 c$m^{3}$

Volume of Hemisphere = 2/3 * $\pi$ * $r^{3}$

=> 2 / 3 * 22 / 7 * 1.4 * 1.4 * 1.4

=> 5.74 c$m^{3}$

As there are two hemispheres volume of both the hemispheres = 2 * 5.74

=> 11.48 c$m^{3}$

Volume of Gulab Jamun = Volume of Cylinder + Volume of both the hemispheres = 13.55 + 11.48

=> 25.03 c$m^{3}$

Volume of 50 Gulab Jamun = 50 * 25.03 c$m^{3}$

=>  1,251.5 c$m^{3}$

Given Quantity of Syrup in Gulab Jamun = 40 %

Syrup in 50 gulab jamuns = 40% of volume of 50 Gulab Jamuns

=> 40 / 100 * 1,251.5 = 500.6 c$m^{3}$

Therefore, the Syrup in 50 Gulab Jamuns is 500.6 c$m^{3}$