Question

four right cylindrical vessels each having diameter 21 cm and hieght 38 cm are full of ice cream. the icecream is to be filles in cones of hieght 12 cm and diameter 7cm having hemispherical shape on top. find the total number of such cones which can be filled with icecream.

Answer 1

diameter of cylindrical vessel= 21cm

radius= 21/2= 10.5cm

height = 38cm

volume of vessel =

$\pi \: r \: ^{2} h$

= 22/7 x (10.5)^2 x 38

= 13167cm^3

if there are 4 cylindrical vessels then total volume= 4 x 13167

= 52668cm^3

Now, height of cone= 12cm

diameter=7cm

radius= 7/2 = 3.5cm

volume of cone=

$1 \div 3\pi \: r^{2} h$

= 1/3 x 22/7 x (3.5)^2 x 12

= 154 cm^3

no. of cones that can be filled= 52668/154

=342

So, 342 cones can be filled with ice creams