Yurt Geometry and Scale Modeling Exercise

This page presents a comprehensive exercice type brevet maths avec corrigé PDF focusing on the geometry of a yurt-shaped structure and related scale modeling problems. The exercise is divided into several parts, each addressing different mathematical concepts applicable to the brevet exam.

The first part of the exercise deals with calculating the floor area of the yurt. The solution demonstrates how to determine the radius from the given diameter and then apply the formula for the area of a circle. This section also includes a comparison with an apartment size.

Example: The yurt's diameter is 7 meters, so the radius R = D/2 = 7/2 = 3.5 meters. The area is then calculated using A = πR² = π × 3.5² ≈ 38.5 m².

The second part focuses on volume calculations. It involves finding the total volume of the yurt by combining the volumes of a cylinder (for the walls) and a cone (for the roof).

Highlight: The total volume is calculated using the formula V = V₁ + V₂, where V₁ is the volume of the cylindrical part and V₂ is the volume of the conical roof.

The third section introduces a scale modeling problem, demonstrating the application of proportionality in creating accurate miniature representations.

Vocabulary: Scale - A ratio that shows the relationship between the size of something on a model or map and its actual size.

The exercise concludes with calculations related to the scale model, including determining the height of the model based on the given scale ratio.

Definition: Proportionality - A relationship between quantities where one quantity changes in direct proportion to the change in another quantity.

This exercice BREVET volume pdf effectively combines multiple mathematical concepts, providing students with a comprehensive review of geometry and proportionality in preparation for the brevet exam.