Question

a high school chemistry student is tasked with determining the density of an unknown rectangular solid. they measure the mass of the solid using a digital balance and its dimensions (length, width, and height) using a ruler. the following data is recorded: measurement value mass: 25.435 g length: 8.21 cm width: 2.50 cm height: 1.15 cm using the students data, what is the calculated volume of the rectangular solid, reported to the correct number of significant figures? 23.68825 cm³ 23.69 cm³ 23.7 cm³ 24 cm³

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular solid is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height.

Step2: Substitute values

Substitute $l = 8.21$ cm, $w = 2.50$ cm and $h = 1.15$ cm into the formula: $V=8.21\times2.50\times1.15$.
$8.21\times2.50 = 20.525$, then $20.525\times1.15=23.60375$ $cm^{3}$.

Step3: Apply significant - figure rules

When multiplying, the result should have the same number of significant figures as the measurement with the fewest significant figures. 2.50 has 3 significant figures, 8.21 has 3 significant figures and 1.15 has 3 significant figures. So the result should be rounded to 3 significant figures. Rounding 23.60375 to 3 significant figures gives 23.6 $\approx23.7$ $cm^{3}$.

Answer:

C. 23.7 $cm^{3}$