A cereal box has a base of 3 inches by 5 inches and is 10 inches tall. Another box has a base of 5 inches by 6 inches. What formula is necessary for students to use to find out how tall the second box would need to be in order to hold the same amount of cereal?

To determine how tall the second box needs to be in order to hold the same amount of cereal as the first box, students must first calculate the volume of the first box. The formula for the volume of a rectangular solid is given by the product of its base area and its height.

The first box dimensions are 3 inches by 5 inches for the base and 10 inches tall, which gives a volume calculated as:

Volume = Base Area × Height

Base Area = Length × Width = 3 inches × 5 inches = 15 square inches

Volume of the first box = 15 square inches × 10 inches = 150 cubic inches.

For the second box, the base area is 5 inches by 6 inches. To find the required height that enables the second box to have the same volume of 150 cubic inches, students will set up the equation:

Volume = Base Area × Height

150 cubic inches = (5 inches × 6 inches) × Height.

Thus, the second box must have a volume calculated using the same principles, and the need to find height reinforces the necessity of using the volume of a rectangular solid formula. By rearranging the equation to solve for height, students can find the answer.

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