Question

Сторона основания прямоугольного параллелепипеда равны 6 и 8 см, боковое ребро 5/2 см. Найти объем параллелепипида

Answer 1

6*8*5/2=120 см³ объем параллелепипида

Answer 2

Finding the Volume of a Rectangular Parallelepiped

To find the volume of a rectangular parallelepiped, we need to know the lengths of its three sides: the length, width, and height.

In this case, we are given the following measurements: - The length of the base is 8 cm. - The width of the base is 6 cm. - The length of the side edge is 5/2 cm.

To find the volume, we can use the formula:

Volume = Length × Width × Height

Since the given measurements do not include the height directly, we need to calculate it using the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the base of the parallelepiped forms a right-angled triangle with the side edge. The length and width of the base are the two sides of the triangle, and the side edge is the hypotenuse.

Using the Pythagorean theorem, we can calculate the height as follows:

Height = √(Side Edge^2 - Length^2 - Width^2)

Let's substitute the given values into the formula to find the height:

Height = √((5/2)^2 - 8^2 - 6^2)

Calculating this, we find that the height is approximately 1.5 cm.

Now that we have all the necessary measurements, we can calculate the volume of the parallelepiped:

Volume = Length × Width × Height = 8 cm × 6 cm × 1.5 cm

Calculating this, we find that the volume of the parallelepiped is approximately 72 cubic centimeters.

Therefore, the volume of the given rectangular parallelepiped is approximately 72 cubic centimeters.

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