Solve the problem. Round your answer to two decimal places.
-The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 128 g, find the weight of the liquid in a cubical container 5 cm on a side.
A) 250 g
B) 105 g
C)10g
D) 125 g

Question

Quizplus · Accepted Answer

The weight of the liquid is directly proportional to its volume. The volume of a cube is given by $V = s^3$, where $s$ is the side length. For the first cube, $V_1 = 4^3 = 64 \, \text{cm}^3$, and its weight is 128 g. For the second cube, $V_2 = 5^3 = 125 \, \text{cm}^3$. Since the weight varies directly with volume, we can set up a proportion: $\frac{128 \, \text{g}}{64 \, \text{cm}^3} = \frac{W_2}{125 \, \text{cm}^3}$, solving for $W_2$ gives $W_2 = \frac{128 \times 125}{64} = 250 \, \text{g}$.

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