Question

An ice cream machine has two taps for filling ice cream cones of height $12cm$ and radius $3.5cm$. If the flow rate of ice cream from both taps is equal to $6.16c{m}^3/s$, find the maximum number of cones that can be filled by the machine in an hour.
[Given: $\pi =\frac{22}{7}$]

Answer 1

Given: Number of taps $=2$
Specification of ice cream cone: $r=3.5cm$, $h=12cm$
Flow rate of ice cream from taps $=6.16c{m}^3/s$
Now,
Volume of an ice cream cone $=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times {3.5}^2\times 12$
$=154c{m}^3$
Volume of ice cream coming out of a tap in an hour $=6.16\times 3600c{m}^3=22176c{m}^3$
Maximum number of cone that can be filled by a tap in an hour $=\frac{22176}{154}=144$
Maximum number of cones that can be filled by the machine in an hour $=2\times 144=288$ (∵ there are two taps)