Suppose you magically tripled in size. That​ is, your​ height, width, and depth increased by a factor of 3. By what factor has the amount of material required for your clothes​ increased?

When your height, width, and depth all triple in size, the amount of material required for your clothes depends on the surface area of your body. 

### Explanation:

- Your clothes cover the surface of your body, and surface area is a **two-dimensional measure** (like height × width for a rectangle or \( 4 \pi r^2 \) for a sphere's surface).
- Surface area scales with the square of the linear dimensions. This means if your height, width, and depth are tripled, the surface area increases by a factor of \( 3^2 = 9 \).

Thus, the amount of material required for your clothes would increase by a factor of **9**.

Would you like more details or have any questions?

---

Here are 5 related questions to expand on this concept:

1. How would the volume of your body change if all dimensions tripled?
2. If you doubled in size instead of tripling, by what factor would the surface area increase?
3. What mathematical relationship exists between volume and scaling of linear dimensions?
4. How does this principle apply to other objects, such as scaling a cube?
5. Can you calculate how mass changes with scaling if density remains constant?

**Tip:** When scaling objects, always consider whether the question involves **surface area** (2D) or **volume** (3D) since they scale differently.

Discover how tripling your height, width, and depth affects the amount of material needed for clothing. Learn the relationship between surface area and scaling, with key concepts like geometry and the surface area formula. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation