Question

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

Explanation:

Step1: Calculate volume of container A

The volume of a cube \(V = s^3\), where \(s = 15\) cm. So \(V_A=15^3=3375\) \(cm^3\).

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 \(V_B=14\times12\times10 = 1680\) \(cm^3\).

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 \(V_C=\frac{4}{3}\pi(4)^3=\frac{4}{3}\pi\times64\approx268.08\) \(cm^3\).

Step4: Calculate mass of gas in container A

Using the formula \(m=
ho V\), with \(
ho_A = 0.09\) mg/cm³ and \(V_A = 3375\) \(cm^3\), \(m_A=0.09\times3375 = 303.75\) mg.

Step5: Calculate mass of gas in container B

Using \(
ho_B = 0.175\) mg/cm³ and \(V_B = 1680\) \(cm^3\), \(m_B=0.175\times1680 = 294\) mg.

Step6: Calculate mass of gas in container C

Using \(
ho_C = 1.251\) mg/cm³ and \(V_C\approx268.08\) \(cm^3\), \(m_C=1.251\times268.08\approx335.37\) mg.

Step7: Order the masses

Comparing \(m_A = 303.75\) mg, \(m_B = 294\) mg, and \(m_C\approx335.37\) mg, the order from least to greatest is \(B, A, C\).

Answer:

B, A, C