Q. 34.0( 452 Votes )

# A gulabjamun contains sugar syrup up to about30% of its volume. Find approximately how much syrup would be found in 45 gulabjamun each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see Fig. 13.15)

Answer :

Radius (*r*) of cylindrical part == 1.4 cm

Radius (*R*) of hemispherical part == 1.4 cm

Length of each hemispherical part = 1.4 cm

The radius of hemispherical part = 1.4 cm

Length (*h*) of cylindrical part = 5 - 2 × Length of hemispherical part

= 5 -( 2 × 1.4 )

= 5 - 2.8

= 2.2 cm

The volume of one gulabjamun = Vol. of cylindrical part + 2 × Vol. of hemispherical part

= (πr^{2}h )+ (2 × πR^{3})

= (πr^{2}h) + (R^{3})

= [π × (1.4)^{2} × 2.2] +[ (1.4)^{3}]

=

=

= 13.552 + 11.498

= 25.05 cm^{3}

Volume of 45 gulabjamun = 45 × 25.05

= 1,127.25 cm^{3}

The volume of sugar syrup = 30% of the volume

= × 1127.25

= 338.17 cm^{3}

**= 338 cm ^{3}(approx)**

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PREVIOUSRachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminum sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same)NEXTA pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by3.5 cm. The radius of each of the depressions is 0.5cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 13.16)

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