Question

for the problems below, show all work and box your final answers. 1. a platinum bar measures 5.0 cm long, 4.0 cm wide, and 1.5 cm thick. it has a mass of 700.0 grams. a. calculate the volume of the platinum bar. 30 cm³ b. calculate the density of the platinum bar. 2. a lead cylinder has a mass of 540 grams and a density of 2.70 g/ml. calculate the volume of the lead cylinder.

Explanation:

Step1: Calculate volume of the platinum bar

Use the formula for the volume of a rectangular - prism $V = l\times w\times h$, where $l = 5.0$ cm, $w = 4.0$ cm and $h = 1.5$ cm.
$V=5.0\times4.0\times1.5$
$V = 30$ $cm^{3}$

Step2: Calculate density of the platinum bar

Use the density formula $
ho=\frac{m}{V}$, where $m = 700.0$ g and $V = 30$ $cm^{3}$.
$
ho=\frac{700.0}{30}\approx23.3$ g/$cm^{3}$

Step3: Calculate volume of the lead cylinder

Use the density formula $
ho=\frac{m}{V}$, and re - arrange it to $V=\frac{m}{
ho}$. Given $m = 540$ g and $
ho = 2.70$ g/mL. Since 1 $cm^{3}$=1 mL, $V=\frac{540}{2.70}$
$V = 200$ $cm^{3}$

Answer:

a. The volume of the platinum bar is 30 $cm^{3}$.
b. The density of the platinum bar is approximately 23.3 g/$cm^{3}$.
The volume of the lead cylinder is 200 $cm^{3}$.