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.
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.
