A rectangular block of lead (Pb) measures 20.0 mm X 30.0 mm X 45.0 mm. If the density of Pb is 11.34 g/cm3, calculate the mass of the block.

Question

BlackTom AI · Accepted Answer

We start by restating the problem: a rectangular block of lead has dimensions 20.0 mm by 30.0 mm by 45.0 mm, with a density of 11.34 g/cm^3, and we need to find its mass.

First, convert all linear dimensions from millimeters to centimeters because density is given in g/cm^3. 20.0 mm = 2.0 cm, 30.0 mm = 3.0 cm, and 45.0 mm = 4.5 cm.

Next, calculate the volume of the block using the formula for a rectangular prism: volume = length × width × height. So, V = 2.0 cm × 3.0 cm × 4.5 cm = 27.0 cm^3.

Then, apply mass = density × volume. With density 11.34 g/cm^3 and volume 27.0 cm^3, the mass M = 11.34 g/cm^3 × 27.0 cm^3 = 306.18 g.

Rounding to an appropriate level of precision (two to three significant figures consistent with the given measurements), this is about 306 g. If an option lists 306 g Pb, it would be the closest representation of the calculated mass.

To recap: the key steps were unit conversion (mm to cm), volume calculation of the rectangular block, and multiplication by density to obtain mass. Any deviation in the volume calculation (e.g., mis-converting units) would lead to an incorrect mass, and using an incorrect density would also skew the result. The final numeric result depends on the exact density and dimensions provided, but with the given values, 306 g is the expected mass when rounded to the nearest gram.

A rectangular block of lead (Pb) measures 20.0 mm X 30.0 mm X 45.0 mm. If the density of Pb is 11.34 g/cm3, calculate the mass of the block.单项选择题

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