https://r2.erweima.ai/mathbot/image/1725889113463gbrdz4g5.jpg

This problem involves calculating the volume of a toilet paper roll, modeled as a cylindrical shape with a hollow center (a smaller cylinder subtracted from a larger one).

### Given:
- External diameter = 12 cm
- Internal diameter = 4 cm
- Height = 10 cm

### Approach:
1. First, compute the radii:
   - External radius \( R = \frac{12}{2} = 6 \, \text{cm} \)
   - Internal radius \( r = \frac{4}{2} = 2 \, \text{cm} \)

2. The volume of a cylinder is given by:
   \[
   V = \pi r^2 h
   \]
   The volume of the toilet paper roll can be calculated by subtracting the volume of the inner cylinder (hole) from the outer cylinder (entire roll).

   \[
   V_{\text{roll}} = \pi R^2 h - \pi r^2 h
   \]
   Factoring out \( \pi h \), the equation becomes:
   \[
   V_{\text{roll}} = \pi h (R^2 - r^2)
   \]

Now, let's calculate the exact volume.The volume of the toilet paper roll is approximately 1005.31 cubic centimeters.

Would you like more details on the calculations or have any additional questions?

Here are five related questions to expand your understanding:
1. How would the volume change if the external diameter were increased by 2 cm?
2. What is the impact on volume if the height is doubled while keeping the diameters constant?
3. How do you calculate the surface area of this toilet paper roll?
4. What would the volume be in liters instead of cubic centimeters?
5. How does this concept apply to other hollow cylindrical objects like pipes?

**Tip:** When dealing with hollow shapes, always subtract the inner volume from the outer to find the net volume.

Considere um rolo de papel higiênico com 12 cm de diâmetro externo, 4 cm de diâmetro interno e 10 cm de altura. O volume, em centímetros cúbicos, desse rolo é?

Calculate the volume of a hollow cylindrical toilet paper roll with external diameter 12 cm, internal diameter 4 cm, and height 10 cm. This problem covers cylindrical geometry concepts, including volume subtraction. Ideal for Grades 9-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation