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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

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
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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### 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. \( 150h - 25\pi h\)
Transcribed Image Text:### 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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