Question

В основании прямой призмы лежит квадрат со стороной 7. Боковые ребра равны 2/пи . Найдите объем цилиндра ,описанного около этой призмы.

Answer 1

А=7;Н=2/π;
D=2R=диагонали квадрата,⇒
D=7√2;
V=πD²/4·H=π·49·2/4·2/π=49;

Answer 2

Calculation of the Volume of the Cylinder

To find the volume of the cylinder described around the given prism, we need to determine the height of the cylinder.

Let's analyze the given information step by step:

- The base of the prism is a square with a side length of 7. - The lateral edges of the prism are equal to 2/π.

To find the height of the cylinder, we need to calculate the diagonal of the base square. The diagonal of a square can be found using the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.

Let's calculate the diagonal of the base square:

Step 1: Calculate the length of the diagonal of the base square.

Using the Pythagorean theorem, we have:

diagonal^2 = side^2 + side^2

diagonal^2 = 7^2 + 7^2

diagonal^2 = 49 + 49

diagonal^2 = 98

diagonal = √98

diagonal ≈ 9.899

**Step