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)
Solution:
Let's visualize the shape of Gulab jamun as shown below.
From the above figure, we can see that,
Length of cylindrical part = Length of a Gulab jamun - 2 × radius of the hemispherical part
Also,
Diameter of Gulab jamun = diameter of the cylindrical part
Radius of cylindrical part = radius of hemispherical part
In order to find the volume of sugar syrup in 45 Gulab jamuns, we need to find the volume of all the gulab jamun.
As it’s given a Gulab jamun contains sugar syrup up to about 30% of its volume. We make an assumption to every Gulab jamun contains sugar syrup at 30% of its volume to simplify the calculation.
Volume of sugar syrup = 30% of the volume of 45 gulab jamuns.
Diameter of the Gulab jamun, d = 2.8 cm
Radius of cylindrical part = radius of hemispherical part r = d/2 = 2.8/2 cm = 1.4 cm
Length of cylindrical part, h = 5 cm - 2 × 1.4 cm = 2.2 cm
Volume of one Gulab jamun = volume of cylindrical part + 2 × volume of the hemispherical parts
= πr2h + 2 × 2/3 πr3
= πr2h + 4/3 πr3
= πr2 (h + 4r/3)
= 22/7 × 1.4 cm × 1.4 cm × (2.2 cm + (4/3) × 1.4 cm)
= [22/7 × 1.4 cm × 1.4 cm × (12.2/3 cm)]
= 75.152/3 cm3
Volume of 45 Gulab jamuns = 45 × volume of one Gulab jamun
= 45 × 75.152/3 cm3
= 15 × 75.152 cm3
= 1127.28 cm3
Volume of sugar syrup in 45 Gulab jamuns = 30% of volume of 45 Gulab jamun
= 30/100 × 1127.28 cm3
= 338.184 cm3
Thus, the volume of sugar syrup in 45 cylindrical shaped gulab jamuns is 338 cm3 (approximately).
☛ Check: NCERT Solutions for Class 10 Maths Chapter 13
Video Solution:
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)
NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2 Question 3
Summary:
A gulab jamun, contains sugar syrup up to about 30% of its volume. Approximately 338 cm3 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
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