Question

Площадь поверхности куба равна 96 дм3.Найдите сумму длин всех рёбер куба. (МНЕ НУЖНО РЕШЕНИЕ)

Answer 1

Длина ребра равна
$a = \sqrt[3]{96} = 2 \sqrt{12}$
Сумма длин
$L = 12 * 2 \sqrt{12} =24 \sqrt{12}$

Answer 2

Problem Analysis

We are given that the surface area of a cube is 96 dm^2, and we need to find the sum of the lengths of all the edges of the cube.

Solution

To find the sum of the lengths of all the edges of a cube, we can use the formula:

Sum of edge lengths = 12 * edge length

Let's solve the problem step by step:

Step 1: Convert the given surface area from dm^2 to cm^2. - 1 dm = 10 cm - So, 1 dm^2 = (10 cm)^2 = 100 cm^2

Step 2: Find the length of each edge. - The surface area of a cube is given by the formula: Surface area = 6 * (edge length)^2 - Given that the surface area is 96 cm^2, we can set up the equation: 96 cm^2 = 6 * (edge length)^2 - Solving for the edge length, we get: edge length = sqrt(96 cm^2 / 6) = sqrt(16 cm^2) = 4 cm

Step 3: Find the sum of the lengths of all the edges. - Using the formula mentioned earlier, we can calculate the sum of the lengths of all the edges: Sum of edge lengths = 12 * edge length = 12 * 4 cm = 48 cm

Answer

The sum of the lengths of all the edges of the cube is 48 cm.

Verification

Let's verify the solution using the given surface area of 96 dm^2.

- The surface area of a cube is given by the formula: Surface area = 6 * (edge length)^2 - Substituting the edge length of 4 cm, we get: Surface area = 6 * (4 cm)^2 = 6 * 16 cm^2 = 96 cm^2 - The calculated surface area matches the given surface area, which confirms that the solution is correct.