practice: density calculations\nanswer the following questions. make sure to show all work to receive…
practice: density calculations\nanswer the following questions. make sure to show all work to receive credit. you may need a separate sheet of paper\n1. find the volume of a box measuring 2 cm by 7 cm by 3 cm\n2. an object placed in a graduated cylinder raises the volume from 12.2 ml to 14.5 ml. find the volume of the object\n3. find the volume of a cube measuring 5 cm on each side\n4. find the density of the box in #1 if it has a mass of 20 g\n5. find the density of the object in #2 if it has a mass of 4 g
Answer
Explanation:
Step1: Calculate volume of box in #1
The volume formula for a rectangular - box is $V = l\times w\times h$. Given $l = 2$ cm, $w = 7$ cm, $h = 3$ cm. So $V=2\times7\times3 = 42$ $cm^{3}$.
Step2: Calculate volume of object in #2
The volume of the object is equal to the change in volume of the liquid in the graduated - cylinder. So $V=14.5 - 12.2=2.3$ mL.
Step3: Calculate volume of cube in #3
The volume formula for a cube is $V = s^{3}$, where $s = 5$ cm. So $V = 5\times5\times5=125$ $cm^{3}$.
Step4: Calculate density of box in #4
The density formula is $\rho=\frac{m}{V}$. Given $m = 20$ g and $V = 42$ $cm^{3}$ (from Step 1), so $\rho=\frac{20}{42}\approx0.48$ g/$cm^{3}$.
Step5: Calculate density of object in #5
Given $m = 4$ g and $V = 2.3$ mL (from Step 2), so $\rho=\frac{4}{2.3}\approx1.74$ g/mL.
Answer:
- Volume of box: $42$ $cm^{3}$
- Volume of object: $2.3$ mL
- Volume of cube: $125$ $cm^{3}$
- Density of box: $\frac{20}{42}\approx0.48$ g/$cm^{3}$
- Density of object: $\frac{4}{2.3}\approx1.74$ g/mL