Question

Довжина прямокутного паралелепіпеда дорівнює 10 см, ширина - 3 см, висота - 4,5 см. На скільки збільшиться об’єм паралелепіпеда, якщо кожний його розмір зменшити на 1,5 см? пояснення будь ласка?

Answer 1

Ответ:

10*3*2=30*2=60

Пошаговое объяснение:

Answer 2

Calculating the Volume Change of a Rectangular Parallelepiped

To calculate the change in volume of a rectangular parallelepiped when each of its dimensions is decreased by 1.5 cm, we can follow these steps:

1. Calculate the Initial Volume of the Parallelepiped: - The initial volume of the rectangular parallelepiped can be calculated using the formula: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]

2. Calculate the New Dimensions: - After decreasing each dimension by 1.5 cm, the new length, width, and height can be found by subtracting 1.5 cm from each of the initial dimensions.

3. Calculate the New Volume: - Using the new dimensions, calculate the new volume of the parallelepiped using the same formula as above.

4. Find the Change in Volume: - Finally, find the difference between the initial volume and the new volume to determine the change in volume.

Let's proceed with the calculations.

Calculation

1. Initial Volume: - Given: - Length = 10 cm - Width = 3 cm - Height = 4.5 cm - Using the formula, the initial volume can be calculated as: \[ \text{Volume} = 10 \, \text{cm} \times 3 \, \text{cm} \times 4.5 \, \text{cm} \] \[ \text{Volume} = 135 \, \text{cm}^3 \]

2. New Dimensions: - After decreasing each dimension by 1.5 cm: - New Length = 10 cm - 1.5 cm = 8.5 cm - New Width = 3 cm - 1.5 cm = 1.5 cm - New Height = 4.5 cm - 1.5 cm = 3 cm

3. New Volume: - Using the new dimensions, the new volume can be calculated as: \[ \text{Volume} = 8.5 \, \text{cm} \times 1.5 \, \text{cm} \times 3 \, \text{cm} \] \[ \text{Volume} = 38.25 \, \text{cm}^3 \]

4. Change in Volume: - The change in volume can be found by subtracting the initial volume from the new volume: \[ \text{Change in Volume} = 38.25 \, \text{cm}^3 - 135 \, \text{cm}^3 \] \[ \text{Change in Volume} = -96.75 \, \text{cm}^3 \]

Conclusion

The volume of the rectangular parallelepiped decreases by 96.75 cm³ when each of its dimensions is decreased by 1.5 cm.