drag each tile to the correct box. there are three containers filled with different gases as shown…

drag each tile to the correct box. there are three containers filled with different gases as shown. \n|container|gas density|container dimensions|\n|----|----|----|\n|a|hydrogen - 0.09 mg/cm³|a cube with sides of 15 cm|\n|b|helium - 0.175 mg/cm³|a rectangular prism with sides of 14 cm, 12 cm, 10 cm|\n|c|nitrogen - 1.251 mg/cm³|a sphere with a diameter of 8 cm|\nwhat is the correct order of mass from least to greatest?

drag each tile to the correct box. there are three containers filled with different gases as shown. \n|container|gas density|container dimensions|\n|----|----|----|\n|a|hydrogen - 0.09 mg/cm³|a cube with sides of 15 cm|\n|b|helium - 0.175 mg/cm³|a rectangular prism with sides of 14 cm, 12 cm, 10 cm|\n|c|nitrogen - 1.251 mg/cm³|a sphere with a diameter of 8 cm|\nwhat is the correct order of mass from least to greatest?

Answer

Explanation:

Step1: Calculate volume of container A

The volume of a cube $V = s^3$, where $s = 15$ cm. So $V_A=15^3=3375$ $cm^3$. Then the mass $m_A=\rho_A\times V_A = 0.09\times3375 = 303.75$ mg.

Step2: Calculate volume of container B

The volume of a rectangular - prism $V = l\times w\times h$, where $l = 14$ cm, $w = 12$ cm, $h = 10$ cm. So $V_B=14\times12\times10 = 1680$ $cm^3$. Then the mass $m_B=\rho_B\times V_B=0.175\times1680 = 294$ mg.

Step3: Calculate volume of container C

The volume of a sphere $V=\frac{4}{3}\pi r^3$, with $r=\frac{d}{2}=\frac{8}{2}=4$ cm. So $V_C=\frac{4}{3}\pi(4)^3=\frac{4}{3}\pi\times64\approx268.08$ $cm^3$. Then the mass $m_C=\rho_C\times V_C = 1.251\times268.08\approx335.37$ mg.

Step4: Compare the masses

We have $m_B = 294$ mg, $m_A = 303.75$ mg, $m_C\approx335.37$ mg.

Answer:

B < A < C