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Find the volume of the pyramid. 5 m 18 m cubic meters. www 10 m The volume is

Find the volume of the pyramid. 5 m 18 m cubic meters. www 10 m The volume is

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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### Finding the Volume of a Pyramid To determine the volume of a pyramid, we can use the following geometric formula for the volume of a pyramid: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] #### Given Measurements: - The base of the pyramid is a rectangle with a width of 10 meters and a length of 18 meters. - The height (perpendicular distance from the apex to the center of the base) is 5 meters. ### Step-by-Step Calculation: 1. **Calculate the Base Area (A):** \[ A = \text{length} \times \text{width} \] \[ A = 18 \, \text{m} \times 10 \, \text{m} \] \[ A = 180 \, \text{square meters (m}^2\text{)} \] 2. **Calculate the Volume (V):** \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] \[ V = \frac{1}{3} \times 180 \, \text{m}^2 \times 5 \, \text{m} \] \[ V = \frac{1}{3} \times 900 \, \text{cubic meters (m}^3\text{)} \] \[ V = 300 \, \text{cubic meters (m}^3\text{)} \] ### Graphical Representation: The image displays a 3-dimensional pyramid drawn with dashed lines indicating dimensions: - The base of the pyramid is rectangular with lengths of 10 meters (width) and 18 meters (length). - The height from the center of the base to the apex is marked as 5 meters. ### Final Volume: Thus, the volume of the pyramid is: \[ \text{The volume is } 300 \text{ cubic meters.} \] Understanding these steps allows for solving similar problems by applying appropriate geometric formulas and calculations.
Transcribed Image Text:### Finding the Volume of a Pyramid To determine the volume of a pyramid, we can use the following geometric formula for the volume of a pyramid: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] #### Given Measurements: - The base of the pyramid is a rectangle with a width of 10 meters and a length of 18 meters. - The height (perpendicular distance from the apex to the center of the base) is 5 meters. ### Step-by-Step Calculation: 1. **Calculate the Base Area (A):** \[ A = \text{length} \times \text{width} \] \[ A = 18 \, \text{m} \times 10 \, \text{m} \] \[ A = 180 \, \text{square meters (m}^2\text{)} \] 2. **Calculate the Volume (V):** \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] \[ V = \frac{1}{3} \times 180 \, \text{m}^2 \times 5 \, \text{m} \] \[ V = \frac{1}{3} \times 900 \, \text{cubic meters (m}^3\text{)} \] \[ V = 300 \, \text{cubic meters (m}^3\text{)} \] ### Graphical Representation: The image displays a 3-dimensional pyramid drawn with dashed lines indicating dimensions: - The base of the pyramid is rectangular with lengths of 10 meters (width) and 18 meters (length). - The height from the center of the base to the apex is marked as 5 meters. ### Final Volume: Thus, the volume of the pyramid is: \[ \text{The volume is } 300 \text{ cubic meters.} \] Understanding these steps allows for solving similar problems by applying appropriate geometric formulas and calculations.
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