Question

Площадь диагонального сечения прямоугольного параллелепипеда равна 170 см²; стороны основания равны 8 см и 15 см. Вычисли объём. см3. V = Ответить!

Answer 1

Ответ:

Площадь диагонального сечения прямоугольного параллелепипеда равна произведению диагонали основания на высоту:

S = a * b = 8 см * 15 см = 120 см²

S = diagonal * height

По теореме Пифагора находим диагональ основания:

d = √(a² + b²) = √(8² + 15²) = √(64 + 225) = √289 = 17 см

Тогда:

V = S * h = 170 см² * (17 см / 2) = 1445 см³

Ответ: 1445 см³

Answer 2

Calculation of the Volume of a Rectangular Parallelepiped

To calculate the volume of a rectangular parallelepiped, we need to know the area of the diagonal cross-section and the lengths of the base sides. In this case, the area of the diagonal cross-section is given as 170 cm², and the lengths of the base sides are 8 cm and 15 cm.

Let's calculate the volume using the given information.

The formula for the volume of a rectangular parallelepiped is:

V = length × width × height

In this case, the length and width are the lengths of the base sides, and the height is the distance between the base sides.

Given: - Area of diagonal cross-section = 170 cm² - Length of base side 1 = 8 cm - Length of base side 2 = 15 cm

To find the height, we can use the formula for the area of a rectangle:

Area = length × width

The area of the diagonal cross-section is equal to the product of the length and width of the base sides:

170 cm² = 8 cm × 15 cm

Now, let's solve for the height:

Height = Area / (Length of base side 1)

Height = 170 cm² / 8 cm

Calculating the height:

Height = 21.25 cm

Now that we have the length, width, and height, we can calculate the volume:

V = 8 cm × 15 cm × 21.25 cm

Calculating the volume:

V = 2550 cm³

Therefore, the volume of the rectangular parallelepiped is 2550 cm³.

Please let me know if you need any further assistance!