The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container $4 \mathrm{~cm}$ on a side is 192 grams, find the weight of the liquid in a cubical container $5 \mathrm{~cm}$ on a side.
A) 125 grams
B) 105 grams
C) 375 grams
D) 15 grams

Question

Quizplus · Accepted Answer

The weight of a liquid varies directly with its volume, meaning if the volume increases, the weight increases in the same ratio. The volume of a cube is given by $V = s^3$, where $s$ is the side length of the cube. For the first cube with a side of $4 \mathrm{~cm}$, the volume is $4^3 = 64 \mathrm{~cm}^3$, and its weight is 192 grams. This gives us a ratio of weight to volume as $192 \mathrm{~grams} / 64 \mathrm{~cm}^3 = 3 \mathrm{~grams/cm}^3$. For the second cube with a side of $5 \mathrm{~cm}$, the volume is $5^3 = 125 \mathrm{~cm}^3$. Using the same ratio of $3 \mathrm{~grams/cm}^3$, the weight of the liquid in the second cube is $125 \mathrm{~cm}^3 \times 3 \mathrm{~grams/cm}^3 = 375 \mathrm{~grams}$.

The Weight of a Liquid Varies Directly as Its Volume 4 cm4 \mathrm{~cm}4 cm

The Weight of a Liquid Varies Directly as Its Volume $4 \mathrm{~cm}$