Question

Gulab Jamun contains sugar syrup up to about 30% of its volume find it proximately how much syrup will be found in 45 Gulab Jamun 8 shaped like a cylinder with hemispherical ends with length 5 cm and diameter 2.8 centimetre ​

Answer 1

AnswEr :

$\star\:\sf\underline\red{Given:-}$

$\:\:\bullet$ Radius of cylinder = Radius of hemisphere = $\normalsize\sf\frac{2.8}{2} = 1.4cm$

$\:\:\bullet$ Length of hemisphere = Radius of hemisphere = $\normalsize\sf\ 1.4cm$

$\:\:\bullet$Length of cylinder = 5 - 2 $\times$Length of hemisphere = 5 - 2 $\times$ = $\normalsize\sf\ 2.2cm$

$\star\:\sf\underline\red{To \: find:-}$

$\:\:\bullet$ Volume of sugar syrup

$\rule{150}1$

$\star\:\sf\underline\red{Solution :-}$

$\underline{\dag\:\textsf{Calculation \: of \: volume \: of \: Gulabjamun: }}$

$\normalsize\hookrightarrow\sf\purple{Volume_{Gulanjuman} } \: = \: \red{Volume_{cylindrical \: portion} } + \green{2 \times\ Volume_{hemispherical \: part} }$

$\normalsize\hookrightarrow\sf\purple{Volume_{Gulabjuman} }\: = \: \red{\pi r^2h} + \green{2 \times\ \frac{2}{3} \pi r^2h}$

$\normalsize\hookrightarrow\sf\purple{Volume_{Gulabjamun} } =\frac{22}{7}</p><p>\times\ 1.4 \times\ 1.4 \times\ 2.2 + \frac{4}{3} \times\ \frac{22}{7}\times\ 1.4 \times\ 1.4 \times\ 1.4 \\ \\ \normalsize\hookrightarrow\sf\purple{Volume_{Gulabjamun} } = 13.552 + 11.498 = 25.05cm^3$

$\rule{200}2$

$\underline{\dag\:\textsf{Calculation \: of \: volume \: of \: cough \: syrup:}}$

$\:\hookrightarrow\sf\underbrace{ 25.05 \times\ 45 = 1,127.25cm^3}_{\orange{Volume \: of \: 45 \: Gulanjamuns} }$

$\hookrightarrow\sf\underbrace{Volume \: of \: cough \: syrup \: = 30 \: percent \: of \: Volume}_{\large\frac{30}{100} \times\ 1,127.25 = 338.17 cm^3 \: = \: 338cm^3}$

$\Large\hookrightarrow{\underline{\boxed{\sf\green{Volume \: of \: cough \: syrup = 338cm^3}}}}$

Answer 2

❂ $\huge\underline\frak\purple{Given}$❂

☞ Length or height of gulab jamuns

5cm

☞ No. of gulab jamuns = 45

☞ Gulab jamuns shaped like cylinder with two hemisphere ends

☞ Height of cylindercal part

= 5-2.8 = 2.2cm

☞ Diameter of hemisphere or cylinder

2.8cm

☞ Radius of hemisphere or cylinder

1.4cm

❂ $\huge\underline\frak\purple{Solution}$❂

☞ Volume of cylinder

πr²h

$\large\frac{22}{7}{×}{1.4×1.4×2.2}$

$\large{4.4×1.4×2.2}$

13.552cm³

☞ Volume of each hemisphere

2/3πr³

$\large\frac{2}{3}{×}\large\frac{22}{7}{×}{1.4}{×}{1.4}{×}{1.4}$

$\large\frac{44×0.28×1.4}{3}$

$\large\frac{17.248}{3}$cm³

☞ Volume of two hemisphere

$\large{2}{×}$$\large\frac{17.248}{3}$

$\large\frac{34.496}{3}$cm³

☞ Volume of each gulab jamun

volume of two hemisphere+volume of cylinder

$\large\frac{34.496}{3}{+}{13.552}$

$\large\frac{34.496+40.656}{3}$

$\large\frac{75.152}{3}$cm³

☞ Volume of 45 gulab jamuns

$\large\frac{75.152}{3}{×}{45}$

1127.28cm³

☞ Volume of the syrup

$\large\frac{30}{100}$$\large{×}$$\large\frac{112728}{100}$

$\large\frac{338184}{1000}$

338.184cm³