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 cylinder with two hemispherical ends with length 5cm and diameter 2.8cm.

Answer 1

$\boxed{\boxed{\mathbb{ANSWER}}}$

$\huge\boxed{\mathsf{\red{338.175\:cm^3}}}$

Volume of gulab jamun = volume of cylinder ( present in the central portion ) and the volume of the two spheres present at the peripheral ends .

Find the volume of the gulab jamun

Volume of cylinder

Diameter = 2.8 cm

⇒ radius = diameter / 2

⇒ radius = 2.8 cm / 2

⇒ radius = 1.4 cm

Height of the gulab jamun = 5 cm - 2.8 cm

⇒ 2.2 cm

Volume =  π r² h

⇒ 22/7 × ( 1.4 )² × 2.2

⇒ 22/7 × 1.4 × 1.4 × 2.2

⇒ 22 × 0.2 × 1.4 × 2.2

⇒ 4.4 × 1.4 × 2.2

⇒ 13.55 cm³

Volume of 2 hemispheres

Volume = 2 × 2/3 π r³

⇒ 4/3 × 22/7 × ( 1.4 )³

⇒ 4/3 × 22/7 × 1.4 × 1.4 × 1.4

⇒ 4/3 × 22 × 0.2 × 1.4 × 1.4

⇒ 11.5 cm³

Volume of each gulab jamun

Volume = 13.55 + 11.5

⇒ 25.05 cm³

Volume of 45 ones

Volume = 45 × 25.05

⇒ 1127.25

Volume of syrup

Volume = 30 % of 1127.25

⇒ 30/100 × 1127.25

⇒ 1127.25 × 0.3

⇒ 338.175

The volume of syrup is 338.175 cm³ .

Answer 2

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$


$\bf{338 {cm}^{3} \: (approx) }$


$\bf{ \purple {step \: by \: step \: explanation}}$

The radius (r) of spherical ends and the cylindrical part = 1.4 cm

•°• Height (or length ) (h) of cylindrical part

= ( 5 - 2.8) cm

= 2.2 cm

•°• volume of the gulab jamun = πr²h + 4/3 πr³

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


$\sf \implies \frac{22}{7} \times \frac{14}{10} \times \frac{14}{10} \times (2.2 + \frac{4}{3} \times 1.4) {cm}^{3} \\ \\ \sf \implies \frac{22}{7} \times \frac{14}{10} \times \frac{14}{10} \times \frac{122}{30} {cm}^{3} \\ \\ \sf{ \implies \: 25.05 {cm}^{3}}$


Volume of 45 such gulab jamuns

→ 45 × 25.05 cm³

•°• Amount of syrup

$\sf \implies \: 45 \times 25.05 \times \frac{30}{100} \\ \\ \sf \huge \implies \: 338.17 {cm}^{3} \\ \\ \sf \huge \implies 338 {cm}^{3} \large \: (approx)$