math
posted by gaurav on .
The fuel rods for a certain type of nuclear reactor are bundled into a cylindrical shell. Consider this crosssection showing 19 identical fuel rods:
a) If the diameter of the cylindrical shell is 12.35 cm, calculate the shaded area of the crosssection.
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 crosssection of a rod is pi r^2
The crosssection 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 
4189.9

a math for a math