Question

Из единичного куба вырезана правильная четырехугольная призма со стороной основания 0,2 и боковым ребром 1. найдите плошадь поверхности оставшейся части куба

Answer 1

(1*0,2)*4 = 0,8
......

Answer 2

Problem Analysis

We are given a unit cube from which a regular quadrilateral prism with a base side length of 0.2 and a lateral edge length of 1 is cut out. We need to find the surface area of the remaining part of the cube.

Solution

To find the surface area of the remaining part of the cube, we need to subtract the surface area of the cut-out prism from the total surface area of the cube.

The total surface area of the cube is given by the formula: 6s^2, where s is the side length of the cube.

The surface area of the cut-out prism consists of the area of the base and the lateral surface area. The base area is given by the formula: s^2, where s is the side length of the base. The lateral surface area is given by the formula: 4s*l, where s is the side length of the base and l is the lateral edge length.

Let's calculate the surface area of the remaining part of the cube step by step.

1. Calculate the total surface area of the cube: - The side length of the cube is 1, so the total surface area is 6 * 1^2 = 6.

2. Calculate the surface area of the cut-out prism: - The base side length is 0.2, so the base area is 0.2^2 = 0.04. - The lateral edge length is 1, so the lateral surface area is 4 * 0.2 * 1 = 0.8. - The total surface area of the cut-out prism is 0.04 + 0.8 = 0.84.

3. Calculate the surface area of the remaining part of the cube: - Subtract the surface area of the cut-out prism from the total surface area of the cube: 6 - 0.84 = 5.16.

Therefore, the surface area of the remaining part of the cube is 5.16.

Answer

The surface area of the remaining part of the cube is 5.16.