Ex 12.2 Q3 - 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.
Solution:-Given,
Length of gulab jamun = 5 cm
Diameter = 2.8 cm
∴ Radius =
2.8
/
2
= 1.4 cm
➙ From above fig. we can find that,
Radius of cylindrical part = Radius of hemispherical part = r = 1.4 cm
*Height of cylindrical part (h)
= 5 - 2r
= 5 - 2 × 1.4
= 5 - 2.8
= 2.2 cm
➙ Volume of cylindrical part
= πr²h
= π × (1.4)² × 2.2
= π × 1.96 × 2.2
= 4.312π cm³
➙ Volume of Spherical part
=
2
/
3
πr³ =
2
/
3
× π × (1.4)³ =
2
/
3
× π × 2.744 = 1.829π cm³
➙ Volume of one gulab jamun
= Volume of cylindrical part + 2(Volume of
Spherical part)
= 4.312π +2(1.829π)
= 4.312π + 3.658π
= 7.97π
= 7.97 ×
22
/
7
=
175.34
/
7
= 25.05 cm³
➙ Volume of sugar syrup in 45 gulab jamun
= 30% of volume of 45 gulab jamun
=
30
/
100
× 45 × Volume of one gulab jamun =
3
/
10
× 45 × 25.05 = 338.175
~ 338 cm³
Hence,
The volume of sugar syrup in 45 gulab jamuns would be 338 cm³ (approx.)
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Try This..
✒ How much syrup is present in 60 gulab jamuns, each shaped like a cylinder with two hemispherical ends, having a length of 6 cm and diameter of 3 cm, if 25% of their volume is syrup?
✒ A rocket is in the shape of a cone mounted on a cylinder. If the height of the cone is 6 cm and the height of the cylinder is 20 cm, and the radius is 3.5 cm, calculate the total volume.
✒ Find the volume of a cylindrical pipe with hemispherical caps on both ends, if the length of the pipe is 12 cm and the inner diameter is 6 cm.
✒ A capsule is shaped like a cylinder with two hemispherical ends. The total length of the capsule is 10 cm, and its diameter is 4 cm. Find its total volume.
❌ Common Mistakes
Wrong radius calculation:▸ Always halve the diameter to get the radius (don’t forget!).Subtracting the wrong length:▸ The hemispherical ends contribute to the total length, so subtract their total length (not radius!) from the full length to get the cylinder’s height.Mixing units:▸ Ensure all dimensions are in cm or consistent units before calculation.Forgetting to convert percentage:▸ When taking 30%, always divide by 100.
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 12.2
Ex 12.2 Q3 Class 10
Class 10 Ex 12.2 Q3
Class 10 Chap 12 Ex 12.2 Q3
Class 10 Surface Areas And Volumes
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