Question

Опора представляет собой сочетание параллелепипеда и усеченного конуса. Конус большим основанием располагается в центре параллелепипеда. По центру меньших боковых граней параллелепипеда проходят два выреза треугольной призматической формы. Вдоль оси конуса просверлено сквозное отверстие цилиндрической формы диаметром 16 мм. Общая высота опоры - 60 мм. Высота параллелепипеда 15 мм, длина 90 мм, ширина 55 мм. Диаметр нижнего основания конуса 40 мм, верхнего - 30мм. Длина стороны выреза 10 мм.

Answer 1

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Answer 2

Description of the Support Structure

The support structure described consists of a combination of a parallelepiped and a truncated cone. The larger base of the cone is located at the center of the parallelepiped. There are two triangular prism-shaped cutouts along the center of the smaller lateral faces of the parallelepiped. Additionally, there is a cylindrical through-hole with a diameter of 16 mm drilled along the axis of the cone. The overall height of the support structure is 60 mm, with the parallelepiped having a height of 15 mm, a length of 90 mm, and a width of 55 mm. The diameter of the bottom base of the cone is 40 mm, while the top base has a diameter of 30 mm. The length of the cutout side is 10 mm.

Calculation of the Volume

To calculate the volume of the support structure, we need to find the volumes of the parallelepiped and the truncated cone separately and then add them together.

The volume of a parallelepiped is calculated by multiplying its length, width, and height. In this case, the volume of the parallelepiped is:

Volume of parallelepiped = length * width * height = 90 mm * 55 mm * 15 mm

The volume of a truncated cone is calculated using the formula:

Volume of truncated cone = (1/3) * π * (r1^2 + r2^2 + r1 * r2) * h

where r1 and r2 are the radii of the top and bottom bases of the cone, and h is the height of the cone.

In this case, the volume of the truncated cone is:

Volume of truncated cone = (1/3) * π * (30 mm^2 + 40 mm^2 + 30 mm * 40 mm) * (60 mm - 15 mm)

Finally, we can calculate the total volume of the support structure by adding the volumes of the parallelepiped and the truncated cone.

Total volume = Volume of parallelepiped + Volume of truncated cone

Please note that the above calculations are based on the given dimensions and formulas.