Question

Стороны основания прямоугольного параллелепипеда равны 6 и 8см,а диагональ меньшей боковой грани равна 10см.Найдите объём параллелепипеда.

Answer 1

сначало находишь площадь оснавания: 6*8= 48(см)^2 Затем находишь высоту из прямоугольного треугольника: h=10^2-6^2=8(см) После этого подставляешь в ф-лу: V=S*H=48*8=384(см)

Answer 2

Given Information

We are given that the sides of a rectangular parallelepiped (also known as a rectangular prism) have lengths of 6 cm and 8 cm. The length of the diagonal of the smaller side is 10 cm. We need to find the volume of the parallelepiped.

Solution

To find the volume of a rectangular parallelepiped, we can use the formula:

Volume = length × width × height

In this case, the length and width of the parallelepiped are given as 6 cm and 8 cm, respectively. We need to find the height.

Let's denote the height of the parallelepiped as 'h'. We can use the Pythagorean theorem to find the height.

According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the smaller side of the parallelepiped is the hypotenuse, and the sides of the parallelepiped are the other two sides.

Using the Pythagorean theorem, we have:

h^2 = 6^2 + 8^2

Simplifying the equation, we get:

h^2 = 36 + 64

h^2 = 100

Taking the square root of both sides, we find:

h = 10

Now that we have the height of the parallelepiped, we can calculate the volume using the formula:

Volume = length × width × height

Substituting the given values, we have:

Volume = 6 cm × 8 cm × 10 cm

Simplifying the expression, we get:

Volume = 480 cm^3

Therefore, the volume of the parallelepiped is 480 cubic centimeters.

Answer

The volume of the rectangular parallelepiped is 480 cubic centimeters.