# math

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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?

• math -

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

• math -

4189.9

• math -

a math for a math

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