Question

An ice-cream machine has two taps for filling ice-cream cones of height 6 cm and radius 3 cm. If the flow rate of ice-cream from both taps is equal to 2 $c{m}^3{s}^{-1}$. Find the maximum number of cones machine can fill in an hour.

• A. 255
• B. 248
• C. 258
• D. 260

Answer 1

The correct option is B

248

Volume of one ice-cream cone
$=\frac{1}{3}\pi \times r^2\times h=\frac{1}{3}\pi \times 3^2\times 6=18\pi {\text{cm}}^3$

​Time required to fill each cone
$=\frac{\text{Volume of one ice cream cone}}{\text{Flow rate in one tap}}=\frac{18\pi {\text{cm}}^3}{2{\text{cm}}^3/\text{s}}=9\pi =9\times 3.14=28.26$

The next whole number after 28 is 29.

So, time required to fill each cone is 29 s.

So, in $29\text{s}$ two cones are filled by two taps.

Number of cones that can be filled in 1 hour.
$=\frac{\text{1 hour}}{\text{Time to fill one cone}}\times 2=\frac{3600}{29}\times 2=248.28$
($\because$ 1 h = 3600 s)

Hence, in an hour, it can fill 248 ice-cream cones.