Question

Ширина прямоугольного параллелепипеда 4 целы 1/2 см длина в 1 целых 5/27 раза больше чем длина высота в 3/8 раза больше чем длина. Найдите его объем ПОМОГИТЕ ПОЖАЛУЙСТА

Answer 1

... длина в 1 5/27 раза больше, чем ширина.

4 1/2 * 1 5/27=9/2 * 32/27=16/3=5 1/3 (см) - длина
16/3 * 3/8=2 (см) - высота
4 1/2 * 5 1/3 * 2=9/2 * 16/3 * 2=48(см³) - объем

Answer 2

Calculation of the Volume of a Rectangular Parallelepiped

To find the volume of a rectangular parallelepiped, we need to know its length, width, and height. Let's break down the given information and calculate the volume step by step.

Given information: - Width: 4 1/2 cm - Length: 1 5/27 times the height - Height: 3/8 times the length

Calculating the Length, Height, and Volume

1. Calculating the Length: - The length is 1 5/27 times the height. - Let's assume the height is h cm. - Therefore, the length is (1 5/27) * h cm.

2. Calculating the Height: - The height is 3/8 times the length. - Substituting the length value from step 1, we get (3/8) * [(1 5/27) * h] cm.

3. Calculating the Volume: - The volume of a rectangular parallelepiped is given by the formula V = length * width * height. - Substituting the values we calculated for length, width, and height, we get V = [(1 5/27) * h] * (4 1/2) * [(3/8) * [(1 5/27) * h]] cm^3.

Now, let's simplify the expression and calculate the volume.

Simplifying the Expression and Calculating the Volume

To simplify the expression, we need to convert all the mixed numbers into improper fractions.

1. Converting the Length to an Improper Fraction: - The length is (1 5/27) times the height. - Converting 1 5/27 to an improper fraction: (1 * 27 + 5) / 27 = 32/27. - Therefore, the length is (32/27) * h cm.

2. Converting the Width to an Improper Fraction: - The width is 4 1/2 cm. - Converting 4 1/2 to an improper fraction: (4 * 2 + 1) / 2 = 9/2.

3. Converting the Height to an Improper Fraction: - The height is (3/8) times the length. - Substituting the length value from step 1, we get (3/8) * [(32/27) * h]. - Simplifying the expression: (3/8) * (32/27) * h = (3 * 32 * h) / (8 * 27) = (96h) / 216 = (8h) / 18 = (4h) / 9.

Now, let's substitute the simplified values into the volume formula and calculate the volume.

Calculating the Volume

The volume of the rectangular parallelepiped is given by V = (32/27) * h * (9/2) * (4h/9) cm^3.

Simplifying the expression: V = (32/27) * (9/2) * (4h/9) cm^3 V = (32 * 9 * 4h) / (27 * 2 * 9) cm^3 V = (32 * 4h) / (2 * 27) cm^3 V = (128h) / 54 cm^3 V = (64h) / 27 cm^3

Therefore, the volume of the rectangular parallelepiped is (64h) / 27 cm^3.

Please note that we cannot calculate the exact volume without knowing the value of the height (h). If you provide the value of the height, we can substitute it into the formula to find the volume.