In order to calculate the mass of the gold block, we need to know the volume. To calculate the volume, we need to know the area of the prism's base. Well, we have to start somewhere. The trapezoidal base can be split up into two identical right triangles and a rectangle. The area of the rectangle is length times width, or 14 meters times 16 meters. *A*_{rectangle} = *l* × *w* = (14 m)(16 m) = 224 m^{2}
The base of each triangle is 3 meters and the height is 16 meters.
Each triangle is 24 m^{2}, so two of them make 48 m^{2}. Adding 224 m^{2} and 48 m^{2} gives us 272 m^{2} for the area of the base. Phew. The basic volume formula is: *V* = *Bh*
You don't have to be a rocket scientist to plug in the numbers. It might help, but you don't *have* to be one. *V* = (272 m^{2})(35 m) = 9520 m^{3}
Next is finding the mass. Since the density is given in grams per cubic centimeter, we need to convert cubic meter to cubic centimeter. That's done like this:
Now we can multiply by the volume by the density to get mass. Here we go. Mass = *V* × *d* = (9,520,000,000 cm^{3})(19.3 g/cm^{3}) Mass = 183,736,000,000 g = 1.84 × 10^{8} kg That's a lot of gold. We love gold. |