Question

В шар радиусом 4 см вписан куб. Найти площадь поверхности куба в см2

Answer 1

Есть формулы для куба: радиус описанной сферы равен R=[(√3)/2]*a, где а - сторона куба (другими словами, диаметр описанной сферы - это диагональ куба). Отсюда сторона нашего куба равна а=2R/√3. Площадь поверхности куба равна S=6a² = 6*4*16/3=128cм²

Answer 2

Finding the Surface Area of a Cube Inscribed in a Sphere

To find the surface area of a cube inscribed in a sphere with a radius of 4 cm, we can use the following steps:

1. Determine the length of the cube's edge. 2. Calculate the surface area of the cube.

Let's go through each step in detail.

Step 1: Determine the Length of the Cube's Edge

Since the cube is inscribed in a sphere, the diagonal of the cube is equal to the diameter of the sphere, which is twice the radius. Therefore, the diagonal of the cube is 8 cm.

To find the length of the cube's edge, we can use the formula for the diagonal of a cube in terms of its edge length:

Diagonal of a Cube = √3 * Edge Length

Solving for the edge length, we have:

Edge Length = Diagonal of a Cube / √3

Substituting the value of the diagonal (8 cm) into the formula, we get:

Edge Length = 8 cm / √3

Calculating this value, we find that the length of the cube's edge is approximately 4.6188 cm.

Step 2: Calculate the Surface Area of the Cube

The surface area of a cube is given by the formula:

Surface Area = 6 * (Edge Length)^2

Substituting the value of the edge length (4.6188 cm) into the formula, we get:

Surface Area = 6 * (4.6188 cm)^2

Calculating this value, we find that the surface area of the cube is approximately 267.9497 cm².

Therefore, the surface area of the cube inscribed in a sphere with a radius of 4 cm is approximately 267.9497 cm².