Question

1. e tâche

la casserole dans laquelle maxime a préparé sa colle a un diamètre de 24 cm.
sachant que le côté du carré sur le plan représente 4 cm dans la réalité,
tracer sur le plan suivant le cercle représentant louverture de la casserole
de maxime.

Explanation:

Step 1: Determine the scale factor

The side of the square on the plan represents 4 cm in reality, and the diameter of the circle (casserole opening) in reality is 24 cm. First, we find the scale factor of the plan. Let the side of the square on the plan be \( s_{plan} \) and in reality be \( s_{real} = 4 \) cm. But we need to find the length on the plan corresponding to the real diameter. Let the length on the plan for the diameter be \( d_{plan} \) and real diameter \( d_{real} = 24 \) cm. The scale is \( \frac{s_{real}}{s_{plan}} \), but we can also think of the ratio of real to plan for the square side, and apply it to the diameter. Wait, actually, the square's side on the plan: let's assume the square on the plan has a side length (in plan units, like grid squares) such that in reality it's 4 cm. But maybe the problem is to find the diameter on the plan. Wait, the problem says "tracer sur le plan suivant le cercle représentant l'ouverture de la casserole", knowing that the square's side on the plan represents 4 cm in reality, and the casserole's opening has a diameter of 24 cm in reality. So we need to find the diameter on the plan.

The scale is \( \frac{\text{real length}}{\text{plan length}} = \frac{4 \text{ cm}}{\text{side of square on plan}} \), but actually, we can find the plan length for the diameter by using the ratio. Let \( x \) be the diameter on the plan. Then \( \frac{4 \text{ cm}}{\text{side of square on plan}} = \frac{24 \text{ cm}}{x} \)? Wait, no, maybe the square on the plan: if the square's side on the plan is, say, let's look at the grid. The grid has squares, let's assume each square on the plan has a side length such that in reality, that side is 4 cm. So the scale is \( \text{plan length} : \text{real length} = 1 : \frac{4 \text{ cm}}{\text{plan square side}} \). But maybe the square on the plan is, for example, if the real square side is 4 cm, and on the plan, the square is, say, 1 grid square? Wait, the image shows a grid. Let's assume that the side of the square on the plan (the grid square) corresponds to 4 cm in reality. So the scale is \( \text{plan} : \text{real} = 1 \text{ grid square} : 4 \text{ cm} \). Then the real diameter is 24 cm, so the plan diameter is \( \frac{24 \text{ cm}}{4 \text{ cm per grid square}} = 6 \text{ grid squares} \). So we need to draw a circle with diameter 6 grid squares (or radius 3 grid squares) on the plan.

Wait, let's rephrase:

Real diameter \( d_{real} = 24 \) cm.

Real square side \( s_{real} = 4 \) cm.

The ratio of real diameter to real square side is \( \frac{d_{real}}{s_{real}} = \frac{24}{4} = 6 \). So the diameter on the plan should be 6 times the side of the square on the plan. If the square on the plan has a side length (in plan units, like the length of one grid square), then the diameter on the plan is 6 times that side length. So if the square on the plan is, say, 1 grid square in side length, then the diameter on the plan is 6 grid squares. So we draw a circle with diameter 6 grid squares (radius 3 grid squares) on the plan.

Step 2: Calculate the plan diameter

We have \( \frac{d_{real}}{s_{real}} = \frac{24}{4} = 6 \). So the diameter on the plan is 6 times the side of the square on the plan. If the square on the plan is 1 grid square, then the diameter on the plan is 6 grid squares. So we draw a circle with diameter 6 grid squares (or radius 3 grid squares) on the plan.

Answer:

To draw the circle representing the casserole opening on the plan:

1. Determine the scale: The square’s side (real: 4 cm) corresponds to the plan’s square (e.g., 1 grid square).
2. Calculate the plan diameter: \( \frac{\text{Real diameter}}{\text{Real square side}} = \frac{24\ \text{cm}}{4\ \text{cm}} = 6 \) times the plan square’s side.
3. Draw a circle with diameter = 6 grid squares (or radius = 3 grid squares) on the plan.

(Note: The exact grid square count depends on the plan’s grid, but the key is the ratio \( \boldsymbol{\frac{24}{4} = 6} \) for the diameter relative to the square’s side on the plan.)