Barrel of Wine

[umaa]

A barrel of wine is being filled by a worker stepping on grapes. The barrel with a capacity of 50 liters, is currently one-quarter full. He can step on 500 grapes per minute, each grape a sphere of radius 1 cm, but only yielding seventy-five percent of the volume. How long will it take before the barrel is 3/5th full.

Barrel capacity = 50 liters.
Currently 1/4th fill
Can step 500 grapes/min; ie, 500 grapes/60secs;
Each grape is a sphere of radius 1 cm. But giving 75% of its volume.

3/5 - 1/4 = 7/20

7/20 * 50 = 35/2 = 17.5 liters; So, need to find out the time take to fill 17.5 liters

Grape:
1 cm; Volume of a sphere = 4/3 pi*r^3

4/3*pi*(1)^3 = 4/3*pi

75% of its volume. So, 3/4 * 4/3 * pi = pi

500 grapes per min; So. pi*500

If pi*500 ml is for a min, then how long would it take to fill 17.5 liters?

175 secs.

This is what I'm getting. But my answer is wrong. Can you please explain me.

[scoobydooby]

i guess we must have mixed up the units here.

the radius being in cm we get volume in cubic cm. 1 cubic cm is not equal to 1 litre. 1 cubic meter=1litre
so 1 cubic cm= 0.001 litres

so volume of grapes: pi*500/1000=1/2*pi

1/2*pi litres filled 60 secs
=>17.50 litres would get filled in 60/(1/2*pi)*17.50
=>(120/3.14)*17.50
=700 secs (approx)
~11.66 mins