Question

Объем ящика имеющего форму прямоугольного параллелепипеда, равен 300 см3. Площадь дна равна такому количеству см2, сколько составляет 20% от числа, равного объему ящика. Площадь маленькой стенки равна 50% от площади дна. Найдите площадь полной внешней поверхности ящика с крышкой.

Answer 1

Ответ:

280 см²

Решение:

1) 0,2*300 = 60 (см²) - площадь дна (ab)

2) 0,5*60 = 30 (см²) - площадь маленькой стенки (bc)

3) 300:60 = 5 (см) - высота (с)

4) 30:5 = 6 (см) - ширина (b)

5) 60:6 = 10 (см) - длина (а)

6) 2*(60+30+10*5) = 2*(90+50) = 2*140 = 280 (см²) - площадь полной внешней поверхности ящика с крышкой

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Answer 2

Problem Analysis

We are given a rectangular parallelepiped (box) with a volume of 300 cm³. We need to find the total external surface area of the box with a lid. To solve this problem, we need to determine the dimensions of the box.

Solution

Let's assume the length, width, and height of the box are L, W, and H, respectively.

We are given that the volume of the box is 300 cm³, so we have the equation:

L × W × H = 300 We are also given that the area of the base is equal to 20% of the volume of the box. Since the volume is 300 cm³, the area of the base is:

L × W = 0.2 × 300 We are given that the area of one of the smaller walls is 50% of the area of the base. Therefore, the area of one of the smaller walls is:

L × H = 0.5 × (L × W) To find the dimensions of the box, we can solve these equations simultaneously.

Solving the Equations

Let's solve the equations to find the dimensions of the box.

From equation we have:

L × W × H = 300

From equation we have:

L × H = 0.5 × (L × W)

Simplifying equation we get:

2 × L × H = L × W

Dividing both sides by L, we get:

2 × H = W

Now, we can substitute this value of W in equation:

L × (2 × H) × H = 300

Simplifying further, we get:

2 × L × H² = 300

Dividing both sides by 2, we get:

L × H² = 150

Now, we have two equations:

L × W × H = 300

L × H² = 150

We can solve these equations to find the values of L, W, and H.

Calculation

Let's solve the equations to find the dimensions of the box.

From equation L × H² = 150, we can rearrange it to get:

L = 150 / H²

Substituting this value of L in equation L × W × H = 300, we get:

(150 / H²) × W × H = 300

Simplifying further, we get:

W × H³ = 2

Dividing both sides by H³, we get:

W = 2 / H³

Now, we have the values of L and W in terms of H. We can substitute these values in the equation L × W × H = 300 to solve for H.

Substituting the values of L and W, we get:

(150 / H²) × (2 / H³) × H = 300

Simplifying further, we get:

300 × H⁶ = 150 × 2

Simplifying, we get:

H⁶ = 1

Taking the sixth root of both sides, we get:

H = 1

Now that we have the value of H, we can substitute it back into the equations to find the values of L and W.

From equation L = 150 / H², we get:

L = 150 / 1² = 150

From equation W = 2 / H³, we get:

W = 2 / 1³ = 2

Therefore, the dimensions of the box are:

Length (L) = 150 cm

Width (W) = 2 cm

Height (H) = 1 cm

Calculating the Total External Surface Area

To calculate the total external surface area of the box with a lid, we need to consider the six faces of the box.

The total external surface area is given by:

2 × (L × W) + 2 × (L × H) + 2 × (W × H)

Substituting the values of L, W, and H, we get:

2 × (150 × 2) + 2 × (150 × 1) + 2 × (2 × 1)

Simplifying, we get:

600 + 300 + 4 = 904 cm²

Therefore, the total external surface area of the box with a lid is 904 cm².

Answer

The total external surface area of the box with a lid is 904 cm².