Question

a student found the mass of an object to be 26.5 g. to find the volume, the student submerged the object in a graduated cylinder of water. submerging the object in the water in the graduated cylinder increased the water level by 24.1 ml. the density of the object is
a) 1.1 g/ml.
b) 0.909 g/ml.
c) 1.10 g/ml.
d) 1.0906 g/ml.

Explanation:

Step1: Recall density formula

Density ($
ho$) is given by the formula $
ho = \frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Identify values

Mass $m = 26.5$ g, Volume $V = 24.1$ mL (since the volume of the object is equal to the volume of water displaced).

Step3: Calculate density

Substitute the values into the formula: $
ho = \frac{26.5}{24.1} \approx 1.0996 \approx 1.10$ g/mL (considering significant figures, mass has 3 significant figures, volume has 3 significant figures, so the result should have 3 significant figures). Wait, actually, let's do the division precisely: $26.5\div24.1 = 1.099585\approx1.10$ when rounded to three significant figures? Wait, no, 26.5 is three sig figs, 24.1 is three sig figs. The rule for division is that the result has the same number of sig figs as the least precise measurement. Wait, but let's check the options. Option C is 1.10 (three sig figs), option D is 1.0906 (more decimal places). Wait, let's calculate $26.5\div24.1$:

$26.5\div24.1 = \frac{26.5}{24.1} \approx 1.099585\approx1.10$ (three significant figures) or more precisely, 1.0996 which is approximately 1.10 when rounded to three significant figures? Wait, no, 26.5 has three, 24.1 has three. So the answer should have three. Let's check the options:

A) 1.1 (two sig figs)

B) 0.909 (three sig figs, but wrong value)

C) 1.10 (three sig figs)

D) 1.0906 (more decimal places)

Wait, when we calculate $26.5\div24.1$:

24.1 × 1.09 = 24.1×1 + 24.1×0.09 = 24.1 + 2.169 = 26.269

24.1 × 1.10 = 24.1×1 + 24.1×0.10 = 24.1 + 2.41 = 26.51

Oh! Wait, 24.1×1.10 = 26.51, which is very close to 26.5. So 26.5÷24.1 ≈ 1.10 (because 24.1×1.10 = 26.51, which is almost 26.5). So the correct answer is C) 1.10 g/mL. Wait, but let's do the division: 26.5 divided by 24.1. Let's do it step by step:

24.1 goes into 26.5 once (24.1), subtract 24.1 from 26.5, we get 2.4. Bring down a zero (24.0), 24.1 goes into 24.0 zero times. Bring down another zero (240.0), 24.1 goes into 240.0 nine times (24.1×9=216.9), subtract 216.9 from 240.0, get 23.1. Bring down a zero (231.0), 24.1 goes into 231.0 nine times (24.1×9=216.9), subtract, get 14.1. Bring down a zero (141.0), 24.1 goes into 141.0 five times (24.1×5=120.5), subtract, get 20.5. So putting it together: 1.0995..., which is approximately 1.10 when rounded to three significant figures. So the correct option is C.

Answer:

C) 1.10 g/mL