https://r2.erweima.ai/mathbot/image/1726660294135xgps0ji4.jpg

The problem in the image appears to involve a cube and a rectangular parallelepiped (rectangular prism). Here's a step-by-step breakdown of how to approach each part of the problem:

1. **Given Information:**
   - The image shows a cube and a rectangular parallelepiped. The measurements are given in terms of variables \( x \), \( y \), and \( z \).

2. **Problem Breakdown:**
   - **(a)** Find the edge lengths of each geometric figure given their dimensions.
   - **(b)** Determine the volume of each geometric figure.

### Solution:

#### (a) Finding the Edge Lengths:
- For the **rectangular parallelepiped**, the dimensions are labeled as \( x \), \( y \), and \( z \). Assuming \( x = 1 \), \( y = 3 \), and \( z = 5 \) (from the image):
  - The lengths of the edges are:
    - Length (\(x\)) = 1 cm
    - Width (\(y\)) = 3 cm
    - Height (\(z\)) = 5 cm

- For the **cube**, all edge lengths are equal. From the image, it looks like the cube has an edge length of \( x = 1 \) (since it is a cube, all sides are equal).

#### (b) Calculating the Volume:
- The formula for the volume of a **rectangular parallelepiped** is:
  \[
  V_{\text{parallelepiped}} = x \times y \times z
  \]
  Substituting the values:
  \[
  V_{\text{parallelepiped}} = 1 \times 3 \times 5 = 15 \, \text{cm}^3
  \]

- The formula for the volume of a **cube** is:
  \[
  V_{\text{cube}} = x^3
  \]
  Since the edge length \( x = 1 \):
  \[
  V_{\text{cube}} = 1^3 = 1 \, \text{cm}^3
  \]

### Summary of Answers:
1. **Rectangular Parallelepiped Edge Lengths:** 1 cm, 3 cm, 5 cm.
2. **Cube Edge Length:** 1 cm.
3. **Rectangular Parallelepiped Volume:** 15 cm³.
4. **Cube Volume:** 1 cm³.

Would you like more details or have any questions?

### 5 Related Questions:
1. What is the difference between the surface area and volume of a rectangular parallelepiped?
2. How do the properties of a cube change if its edge length is doubled?
3. What other geometric shapes have the same volume formula as a rectangular parallelepiped?
4. How do you find the surface area of a cube?
5. How does changing the dimensions of a rectangular parallelepiped affect its volume?

### Tip:
For any rectangular prism, the volume scales linearly with changes in each of its dimensions. Doubling one dimension will double the volume, while doubling all dimensions will increase the volume eightfold.

O cubo e o paralelepípedo reto retângulo representados têm as medidas de volume calculadas a partir das dimensões fornecidas.

Learn how to calculate the volume of a cube and a rectangular parallelepiped using given dimensions. This problem explores geometry concepts such as edge lengths and volume formulas, suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation