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प्रश्न
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 the given figure). Use [π = 22/7]
उत्तर
It can be observed that
Radius (r) of cylindrical part = Radius (r) of hemispherical part = `2.8/2` = 1.4 cm
Length of each hemispherical part = Radius of hemispherical part = 1.4 cm
Length (h) of cylindrical part = 5 − 2 × Length of hemispherical part
= 5 − 2 × 1.4
= 2.2 cm
Volume of one gulab jamun = Volume of cylindrical part + 2 × Volume of hemispherical part
= `pir^2h+2xx2/3pir^3 = pir^2h+ 4/3pir^3`
= `pixx(1.4)^2 xx 2.2 + 4/3pi (1.4)^2`
= `22/7 xx 1.4 xx 1.4xx2.2+4/3xx22/7xx1.4xx1.4xx1.4`
= 13.552 + 11.498
= 25.05 cm3
Volume of 45 gulab jamuns = 45 × 25.05 = 1,127.25 cm3
It can be observed that
Radius (r) of cylindrical part = Radius (r) of hemispherical part
= `2.8/2`
= 1.4 cm
Length of each hemispherical part = Radius of hemispherical part
= 1.4 cm
Length (h) of cylindrical part
= 5 − 2 × Length of hemispherical part
= 5 − 2 × 1.4
= 2.2 cm
Volume of sugar syrup = 30% of volume
= `30/100 xx 1127.25`
= 338.175 cm3
= 338 cm3
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