Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Concept explainers
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
![**Activity: Finding the Volume of an Irregular Figure**
**Objective:**
Determine the volume of an irregular three-dimensional geometric figure.
**Instructions:**
Examine the provided diagram and use the given measurements to calculate the figure's volume.
**Diagram:**
The diagram depicts a blue, irregularly-shaped three-dimensional figure with the following dimensions:
- The main body resembles an L-shaped block.
- The larger segment of the block has dimensions of \(9 \, \text{cm}\) in height and \(4 \, \text{cm}\) in width.
- On top of this larger segment, there is a smaller block. The smaller block's dimensions are \(3 \, \text{cm}\) in width, \(2 \, \text{cm}\) in height, and \(1 \, \text{cm}\) in depth.
**Task:**
Find the volume of the irregular figure. The volume should be expressed in cubic centimeters (\(\text{cm}^3\)).
**Solution Steps:**
1. Decompose the irregular figure into simpler shapes (i.e., rectangular prisms).
2. Calculate the volume of each rectangular prism individually.
3. Sum the volumes of the simpler shapes to get the total volume of the irregular figure.
**Note:**
Please use the interactive fields provided to enter your answer. Once the volume is calculated, submit your response by clicking "Enter."
**Answer Format:**
\[
[ ? ] \, \text{cm}^3
\]
---
**© Copyright 2003 - 2021 Acellus Corporation. All Rights Reserved**
*Ensure the correct methodology is applied when calculating the volume, and double-check your measurements before submission.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7f04a1a-45ee-492d-ae93-723f96ad8e53%2F48ece118-4e8c-4e8f-9975-cceeb66a120e%2Fg9avp3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Activity: Finding the Volume of an Irregular Figure**
**Objective:**
Determine the volume of an irregular three-dimensional geometric figure.
**Instructions:**
Examine the provided diagram and use the given measurements to calculate the figure's volume.
**Diagram:**
The diagram depicts a blue, irregularly-shaped three-dimensional figure with the following dimensions:
- The main body resembles an L-shaped block.
- The larger segment of the block has dimensions of \(9 \, \text{cm}\) in height and \(4 \, \text{cm}\) in width.
- On top of this larger segment, there is a smaller block. The smaller block's dimensions are \(3 \, \text{cm}\) in width, \(2 \, \text{cm}\) in height, and \(1 \, \text{cm}\) in depth.
**Task:**
Find the volume of the irregular figure. The volume should be expressed in cubic centimeters (\(\text{cm}^3\)).
**Solution Steps:**
1. Decompose the irregular figure into simpler shapes (i.e., rectangular prisms).
2. Calculate the volume of each rectangular prism individually.
3. Sum the volumes of the simpler shapes to get the total volume of the irregular figure.
**Note:**
Please use the interactive fields provided to enter your answer. Once the volume is calculated, submit your response by clicking "Enter."
**Answer Format:**
\[
[ ? ] \, \text{cm}^3
\]
---
**© Copyright 2003 - 2021 Acellus Corporation. All Rights Reserved**
*Ensure the correct methodology is applied when calculating the volume, and double-check your measurements before submission.*
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