Final answer:
To determine if a drink container with a square base area of 25 cm² and a volume of 400 cm³ will fit inside a lunch box, the container's height must be calculated. The height comes out to be 16 cm. Therefore, whether the container fits or not depends on the internal dimensions of the lunch box.
Step-by-step explanation:
The student is asking whether a drink container with a square base area of 25 cm² and a volume of 400 cm³ will fit inside a lunch box. To determine if the container will fit, we need to calculate its height. Since the volume of a cuboid (which in this case is a cube since it has a square base) is calculated by multiplying the area of the base by the height (V = base area × height), we can calculate the height (h) by dividing the volume by the base area (h = V/base area).
Given the volume (V) is 400 cm³ and the base area is 25 cm², we get h = 400 cm³ / 25 cm² = 16 cm. Now that we have the height, the dimensions of the drink container are a square base with sides of 5 cm (since the area of the base is given and is the product of the sides of the square, 5 cm × 5 cm = 25 cm²) and a height of 16 cm.
To determine if the container will fit inside of a lunch box, we would require the internal dimensions of the lunch box. If the lunch box has internal dimensions greater than or equal to these measurements, the container will fit. Therefore, the correct answer would be C) It depends on the dimensions of the lunch box.