Question

1. 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 real diameter of the pot is \( 24 \, \text{cm} \), and on the plan, \( 4 \, \text{cm} \) (side of the square) corresponds to the real size. Wait, actually, we need to find the scale. Let's see: the real diameter is \( 24 \, \text{cm} \), and we need to represent it on the plan where the square's side is \( 4 \, \text{cm} \) (real). Wait, no, the problem says "le côté du carré sur le plan représente \( 4 \, \text{cm} \) dans la réalité" (the side of the square on the plan represents \( 4 \, \text{cm} \) in reality). So the scale is \( \text{Plan} : \text{Reality} = 1 : 4 \) (since \( 1 \) unit on the plan represents \( 4 \, \text{cm} \) in reality).

Step 2: Calculate the diameter on the plan

The real diameter is \( 24 \, \text{cm} \). To find the diameter on the plan, we use the scale. Let \( d \) be the diameter on the plan. Then \( \frac{d}{24} = \frac{1}{4} \) (because \( 1 \) plan unit = \( 4 \) real cm). Solving for \( d \), we get \( d = \frac{24}{4} = 6 \) plan units (where the plan unit is the side of the square). Wait, actually, the diameter on the plan should be \( \frac{24}{4} = 6 \) times the side of the square? Wait, no, the side of the square on the plan is \( 1 \) unit (let's say \( 1 \) square side length), and it represents \( 4 \, \text{cm} \) in reality. So the real diameter is \( 24 \, \text{cm} \), so the number of square side lengths on the plan is \( \frac{24}{4} = 6 \). So the diameter of the circle on the plan is \( 6 \) times the side of the square. So to draw the circle, we need to have a diameter of \( 6 \) square side lengths. So the radius is \( 3 \) square side lengths.

Step 3: Draw the circle

On the grid, each square has a side length (let's assume the grid squares have side length equal to the plan unit). So we need to draw a circle with diameter \( 6 \) grid squares (or radius \( 3 \) grid squares). So we find the center of the circle (for example, the center of the grid area) and then draw a circle with radius \( 3 \) grid squares.

Answer:

To draw the circle representing the pot's opening on the plan:

1. Determine the scale: The side of a square on the plan represents \( 4 \, \text{cm} \) in reality. Thus, the scale is \( 1 \) (plan unit) : \( 4 \, \text{cm} \) (reality).
2. Calculate the plan diameter: The real diameter is \( 24 \, \text{cm} \). Using the scale, the plan diameter is \( \frac{24}{4} = 6 \) plan units (i.e., \( 6 \) square side lengths).
3. Draw the circle: With the center of the circle (e.g., the center of the grid), draw a circle with radius \( \frac{6}{2} = 3 \) square side lengths (since radius \( = \frac{\text{diameter}}{2} \)).

(Note: The actual drawing involves placing the center on the grid and using a compass to draw a circle with radius \( 3 \) grid squares.)