Problema Solution
The cylindrical jar above has a height of 12 centimeters and a radius of 4 centimeters. The jar contains 20 spherical marbles. Each marble has a radius of 0.8 centimeters. Which of the following represents the amount of space in the jar that is NOT occupied by marbles?
Answer provided by our tutors
The volume of the jar is the volume of cylinder with height H = 12 cm and radius R = 4 cm is:
V1 = (R^2*pi)*H
V1 = 4^2*pi*12
V1 = 192pi cm^3
The volume of one marble is the volume of a sphere with radii R = 0.8 cm:
V2 = (4/3)R^3pi
V2 = (4/3)*0.8^3*pi
V2 = 0.6827pi
The volume that 20 marbles occupy is: 20V2
The space that is not occupied by the marbles is:
V1 - 20V2 = 192pi - 20*0.6827pi = (192 - 20*0.6827)pi = 178.346pi = 560 cm^3