https://file.aiquickdraw.com/mathbot/file/1728860075288gyulfcdr.jpg

Find the volume of the figure. Round to the nearest hundredth of a unit. Let 

*a* = 1.5,
 
*b* = 0.5,

 and 

*c* = 2.

  m3

To calculate the volume of the given 3D figure, we can break it down into two rectangular prisms:

### Step 1: Identifying dimensions
- The larger cube has dimensions \( a \times a \times c \), where \( a = 1.5 \, \text{m} \) and \( c = 2 \, \text{m} \).
- The smaller rectangular prism attached to the side has dimensions \( b \times c \times c \), where \( b = 0.5 \, \text{m} \) and \( c = 2 \, \text{m} \).

### Step 2: Calculating the volume of each part
1. **Volume of the larger cube**: 
   \[
   V_1 = a \times a \times c = 1.5 \times 1.5 \times 2 = 4.5 \, \text{m}^3
   \]
   
2. **Volume of the smaller rectangular prism**: 
   \[
   V_2 = b \times c \times c = 0.5 \times 2 \times 2 = 2 \, \text{m}^3
   \]

### Step 3: Total volume
The total volume \( V_{\text{total}} \) is the sum of the volumes of both parts:
\[
V_{\text{total}} = V_1 + V_2 = 4.5 + 2 = 6.5 \, \text{m}^3
\]

Thus, the volume of the figure is approximately **6.50 cubic meters**.

Would you like further details or clarifications?

### Related Questions:
1. How do you find the surface area of this composite shape?
2. What if the dimensions \( a \), \( b \), and \( c \) were doubled? How would that affect the volume?
3. Can you calculate the volume if the shape is hollow?
4. How do the properties of this figure change if we modify only one dimension, say \( b \)?
5. How would you compute the volume if the figure was a prism with a different cross-sectional shape?

### Tip:
Breaking complex 3D figures into simpler geometric shapes, like cubes or prisms, often simplifies volume calculations considerably.

Find the volume of the figure. Round to the nearest hundredth of a unit. Let a = 1.5, b = 0.5, and c = 2.

Learn how to calculate the volume of a composite 3D shape by breaking it into simpler rectangular prisms. This problem uses the dimensions a = 1.5, b = 0.5, and c = 2, and guides you through the step-by-step process. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation