### Problem Statement:Which expression represents the volume of the rectangular prism that is NOT occupied by the cylinder?### Diagram Illustration:A rectangular prism is shown with the dimensions:- Length: 15 units- Width: 10 units- Height: h unitsA cylinder is inscribed inside this rectangular prism with:- Radius of the base: 5 units- Height: h units (same as the height of the rectangular prism)### Choices:A. $ 25\pi rh $B. $ 125\pi h $C. $ (150 - 25\pi)h $D. $ 150h - 25\pi $### Solution Explanation:To find the volume of the rectangular prism that is not occupied by the cylinder:1. **Volume of Rectangular Prism:** - Formula: $V_{\text{prism}} = \text{length} \times \text{width} \times \text{height}$ - Calculation: $15 \times 10 \times h = 150h$2. **Volume of Cylinder:** - Formula: $V_{\text{cylinder}} = \pi \times \text{radius}^2 \times \text{height}$ - Calculation: $\pi \times 5^2 \times h = 25\pi h$3. **Volume of Rectangular Prism Not Occupied by Cylinder:** - Formula: $V_{\text{remaining}} = V_{\text{prism}} - V_{\text{cylinder}}$ - Calculation: $150h - 25\pi h$ So, the expression representing the volume of the rectangular prism not occupied by the cylinder is:### Correct Answer:D. $ 150h - 25\pi h$

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Answered: Which expression represents the volume…

Which expression represents the volume of the rectangular prism that is NOT occupied by the cylinder. 10 15 A. 25rth B. 1257th C. (150 – 257)h D. 150h-2577

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Problem Statement:

Which expression represents the volume of the rectangular prism that is NOT occupied by the cylinder?

### Diagram Illustration:

A rectangular prism is shown with the dimensions:
- Length: 15 units
- Width: 10 units
- Height: h units

A cylinder is inscribed inside this rectangular prism with:
- Radius of the base: 5 units
- Height: h units (same as the height of the rectangular prism)

### Choices:

A. $ 25\pi rh $

B. $ 125\pi h $

C. $ (150 - 25\pi)h $

D. $ 150h - 25\pi $

### Solution Explanation:

To find the volume of the rectangular prism that is not occupied by the cylinder:

1. **Volume of Rectangular Prism:**
- Formula: $V_{\text{prism}} = \text{length} \times \text{width} \times \text{height}$
- Calculation: $15 \times 10 \times h = 150h$

2. **Volume of Cylinder:**
- Formula: $V_{\text{cylinder}} = \pi \times \text{radius}^2 \times \text{height}$
- Calculation: $\pi \times 5^2 \times h = 25\pi h$

3. **Volume of Rectangular Prism Not Occupied by Cylinder:**
- Formula: $V_{\text{remaining}} = V_{\text{prism}} - V_{\text{cylinder}}$
- Calculation: $150h - 25\pi h$

So, the expression representing the volume of the rectangular prism not occupied by the cylinder is:

### Correct Answer:

D. $ 150h - 25\pi h$

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