https://file.aiquickdraw.com/mathbot/file/172709961778107g0v8jn.jpg

The diagram shows a composite solid, which is made of two rectangular prisms stacked on top of each other.

### Step-by-Step Solution:

1. **Bottom Rectangular Prism:**
   - Dimensions: Length = 18 cm, Width = 8 cm, Height = 5 cm (since the total height of the solid is 15 cm, and the height of the top prism is 10 cm).
   - Volume of bottom rectangular prism:
     \[
     V_1 = \text{length} \times \text{width} \times \text{height} = 18 \, \text{cm} \times 8 \, \text{cm} \times 5 \, \text{cm} = 720 \, \text{cm}^3
     \]

2. **Top Rectangular Prism:**
   - Dimensions: Length = 10 cm, Width = 8 cm, Height = 10 cm.
   - Volume of top rectangular prism:
     \[
     V_2 = \text{length} \times \text{width} \times \text{height} = 10 \, \text{cm} \times 8 \, \text{cm} \times 10 \, \text{cm} = 800 \, \text{cm}^3
     \]

3. **Total Volume:**
   \[
   V_{\text{total}} = V_1 + V_2 = 720 \, \text{cm}^3 + 800 \, \text{cm}^3 = 1520 \, \text{cm}^3
   \]

### Final Answer:
The total volume of the solid is \( 1520 \, \text{cm}^3 \).

---

Would you like further clarification on any of the steps?

Here are some related questions to extend your learning:
1. How would the volume change if the dimensions of the top prism were doubled?
2. What is the surface area of the solid?
3. How would you calculate the volume if the solid were a cylinder instead of rectangular prisms?
4. Can you express the formula for the volume of a rectangular prism in general terms?
5. How does the concept of volume differ from surface area?

**Tip:** When dealing with composite solids, break them down into simpler shapes, calculate individual volumes, and then sum them up to find the total.

Calculate the volume, in cm³, of the composite solid made of two rectangular prisms. The dimensions of the bottom prism are 18 cm by 8 cm by 5 cm, and the top prism is 10 cm by 8 cm by 10 cm.

This guide explains how to calculate the volume of a composite solid made of two rectangular prisms. The bottom prism has dimensions of 18 cm × 8 cm × 5 cm, and the top prism is 10 cm × 8 cm × 10 cm. Step-by-step solution provided, perfect for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation