What is the volume of the plate? Monel metal is a corrosion-resistant copper-nic

Question

What is the volume of the plate?

Monel metal is a corrosion-resistant copper-nickel alloy used in the electronics industry. A particular alloy with a density of 8.80 g/cm3 and containing 0.073 % Si by mass is used to make a rectangular plate that is 15.0 cm long, 12.5 cm wide, and 4.50 mm thick and has a 2.50-cm-diameter hole drilled through its center such that the height of the hole is 4.50 mm . The silicon in the plate is a mixture of naturally occurring isotopes. One of the those isotopes is silicon-30, which has an atomic mass of 29.97376 amu. The percent natural abundance, which refers to the atoms of a specific isotope, of silicon-30 is 3.10%.

Explanation / Answer

We are asked to calculate the volume of the plate. So, we have to do nothing with the composition of the plate because

Volume = length (l)× breadth (b) × height (h)

Since a hole is created in the plate, so,

Volume of plate after hole = total vol. of plate - volume of hole

Total volume of plate = l×b×h = 15 cm × 12.5 cm × 0.45 cm

= 84.375 cm^3 ------------(1)

*The units should be same , so 4.50 mm = 0.450 cm

The hole created by drill will have cylindrical shape and volume of cylinder is r^2×h

r- radius of hole = 1/2 ×(2.50 cm) = 1.25 cm

h-height of hole = 4.50mm = 0.450 cm

So, volume = 3.14 × (1.25 cm)^2 × 0.450 cm

= 2.208 cm^3 -------------(2)

So, volume of plate = (1) - (2) = 84.375 cm^3 - 2.208 cm^3

= 82.167 cm^3

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