A steel plate has a mass of 8.516 kg. If its volume is 1089 cm3, what is the density in gm/cm3?
7.82
Density is the mass contained in a unit of volume, given by the relation \(\rho=\dfrac{m}{V}\). To get an answer in gm/cm³, the mass must be in grams and the volume in cubic centimetres.
The mass is given as \(8.516\ \text{kg}\). Converting to grams, \(8.516\times1000 = 8516\ \text{gm}\).
The volume is already in the required unit: \(1089\ \text{cm}^3\).
Substituting into the formula: \(\rho=\dfrac{8516}{1089}\).
Carrying out the division gives \(\rho\approx 7.82\ \text{gm/cm}^3\), which also matches the known density of steel, confirming the result.
The other options do not satisfy the division: 8.50 and 8.00 would need a smaller volume or larger mass, and 7.25 is too low for the given figures, so only 7.82 is consistent with the data.
Hence, the answer is 7.82.
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