posted by gaurav .
The fuel rods for a certain type of nuclear reactor are bundled into a cylindrical shell. Consider this cross-section showing 19 identical fuel rods:
a) If the diameter of the cylindrical shell is 12.35 cm, calculate the shaded area of the cross-section.
b) If the length of the cylindrical shell is 84.50 cm, what is the volume of the shaded space around the fuel rods?
c) What is the volume of a single fuel rod?
Got no diagram, so I have no idea how the rods are packed into the shell.
Anyway, assuming a rod of radius r, the cross-section of a rod is pi r^2
The cross-section of the shell is pi * 12.35^2 = 152.52 pi = 479.16 cm^2
The shaded space is thus 479.16 - 19* pi r^2 = 479.16 - 59.69r^2
Multiply that by 84.50 to get 40489.0 - 5043.8r^2 cm^3
Volume of a single rod (assuming the same length as the shell) is 84.5 * pi r^2 = 265.46 r^2 cm^3
a math for a math