Question

osmium is a chemical element with a density of 22.6 grams per cubic centimeter. a piece of osmium has a volume of 15.1 cubic centimeters. what is the mass of the piece of osmium to the nearest tenth of a gram?
a. 0.7 grams
b. 1.5 grams
c. 337.7 grams
d. 341.3 grams

Explanation:

Step1: Recall the formula for mass

The formula that relates density ($
ho$), mass ($m$), and volume ($V$) is $m=
ho\times V$. Here, the density $
ho = 22.6$ grams per cubic centimeter and the volume $V=15.1$ cubic centimeters.

Step2: Substitute the values into the formula

Substitute $
ho = 22.6$ and $V = 15.1$ into the formula $m=
ho\times V$. So we have $m=22.6\times15.1$.

Step3: Calculate the product

Calculate $22.6\times15.1$.
\[

$$\begin{align*} 22.6\times15.1&=(22 + 0.6)\times(15+0.1)\\ &=22\times15+22\times0.1 + 0.6\times15+0.6\times0.1\\ &=330+2.2+9 + 0.06\\ &=330+9+2.2 + 0.06\\ &=339+2.26\\ &=341.26 \end{align*}$$

\]

Step4: Round to the nearest tenth

Rounding $341.26$ to the nearest tenth. The digit in the hundredth place is $6$, which is greater than or equal to $5$, so we round up the tenths place. So $341.26\approx341.3$.

Answer:

D. 341.3 grams