# Mensuration-62

### From Homeworkwiki

**Four right circular cylindrical vessels each having diameter 21 cm and height 38 cm are full of ice-cream.**

**The ice-cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top.**

**Find the total number of such cones which can be filled with ice-cream.**

**Solution:** Volume of a right circular cylinder = 4/3 Π r^{2} h

Volume of hemisphere = 2/3 Π r^{2}

Volume of cone = Volume of cylinder + Volume of hemisphere = 1/3 Π r^{2} h + 2/3 Π r^{2}

Given, Volume of right circular cylinder = n [Volume of cone + Volume of hemisphere]

Therefore, 4/3 Π r^{2} h = n [1/3 Π r^{2} h + 2/3 Π r^{2}
]

Implies, Π x 21^{2} x 38 = n Π / 3 x 7^{2} / 4 [12 + 2 x 7 / 2]

Implies, 21 x 21 x 38 = (n x 7 x 7) / 12 x 19

Implies, n = (21 x 21 x 38 x 12) / (7 x 7 x 19) = 216.