Math, asked by goutamyadav5070, 7 hours ago

48 3. 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 Fig. 13.15).

Answers

Answered by UrAddiction
117

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Given parameters:

  • Each gulab jamun is given the form of a cylinder with two hemispherical ends.

Diameter of the cylinder = 2.8 cm

Radius of the cylinder = Diameter of cylinder/2

Diameter of the hemisphere = 2.8 cm

Radius of the hemisphere = Diameter of hemisphere/2

Radius of the hemisphere (r) = 2.8 /2

r = 1.4 cm

Height of the cylinder + 2 ✕ Radius of the hemisphere = 5 cm

Height of the cylinder = 5 – (2 ✕ Radius of the hemisphere)

Height of the cylinder = 5 – (2 ✕ 1.4)

Height of the cylinder (h) = 2.2 cm

⠀⠀ ⠀

Volume of Cylinder = πr²h

Volume of cylinder = (22/7) ✕ (1.4)2 ✕ 2.2

Volume of cylinder = 13.552 cm³

Volume of hemisphere = (2/3) πr³

Volume of hemisphere = (2/3) ✕ (22/7) ✕ (1.4)³

Volume of hemisphere = 0.667 ✕ 3.143 ✕ 2.744

Volume of hemisphere = 5.75 cm³

Now

Volume of two hemisphere = 2 ✕ 5.75 cm³

Volume of two hemisphere = 11.5 cm³

Let us calculate the volume of the gulab jamun

Volume of gulab jamun = Volume of the cylinder + Volume of two hemisphere

Volume of gulab jamun = 13.552 cm³ + 11.5 cm³

Volume of gulab jamun = 25.052 cm³

The volume of one gulab jamun is 25.052 cm³

∴ The volume of 45 gulab jamun = 25.052 cm³ ✕ 45

The volume of 45 gulab jamun = 1127.34 cm³

In gulab jamun quantity of sugar syrup = 30% = 30/100 = 0.3

The quantity of sugar syrup in 45 gulab jamun = 0.3 ✕ volume of one gulab jamun ✕ 45

The quantity of sugar syrup in 45 gulab jamun = 0.3 ✕ 25.052 ✕ 45

The quantity of sugar syrup in 45 gulab jamun = 338.25 cm³

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