Question

в правильной четырехугольной призме диагональ боковой грани равна 6 см а боковое ребро 5 см вычислите объем призмы

Answer 1

V=S(основания)*h=корень_из(36-25)^2*5=55

Answer 2

Calculation of the Volume of a Prism

To calculate the volume of a prism, we need to know the area of the base and the height of the prism. In this case, we are given the diagonal of a lateral face and the length of a lateral edge of a right rectangular prism.

Let's break down the problem step by step:

1. We are given that the diagonal of a lateral face is 6 cm. This diagonal represents the hypotenuse of a right triangle formed by the length, width, and height of the prism. 2. We are also given that the length of a lateral edge is 5 cm.

To find the height of the prism, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the length, width, and height of the prism as l, w, and h, respectively.

Using the Pythagorean theorem, we have:

l^2 + w^2 = 6^2

Since we know that the length of a lateral edge is 5 cm, we can substitute l = 5 into the equation:

5^2 + w^2 = 6^2

Simplifying the equation, we get:

25 + w^2 = 36

Subtracting 25 from both sides, we have:

w^2 = 11

Taking the square root of both sides, we find:

w = √11

Now that we have the width of the prism, we can calculate the volume.

The volume of a right rectangular prism is given by the formula:

Volume = length × width × height

In this case, the length is 5 cm, the width is √11 cm, and the height is 6 cm.

Substituting these values into the formula, we get:

Volume = 5 × √11 × 6

Calculating the value, we find:

Volume ≈ 103.92 cm^3

Therefore, the volume of the prism is approximately 103.92 cubic centimeters.

Please note that the calculations provided are based on the given information and assumptions made. If there are any additional details or constraints, the answer may vary.