put in front of her model of a library. How much plaster does she need? 3 cm 6 cm 6 cm 2 cm 4 cm 6 cm 9 cm [ ? ] cm³ Enter poration. All Rights Reserved.
put in front of her model of a library. How much plaster does she need? 3 cm 6 cm 6 cm 2 cm 4 cm 6 cm 9 cm [ ? ] cm³ Enter poration. All Rights Reserved.
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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![### Volume Calculation of a Composite Solid
A student is designing a rectangular solid to place in front of her model of a library. Here is the problem she is trying to solve:
#### Problem Statement:
Put in front of her model of a library. How much plaster does she need?
#### Diagram Explanation:
The shape provided is an L-shaped composite solid with the following dimensions:
- Left section:
- Height: 6 cm
- Width: 4 cm
- Depth (common for the entire figure): 6 cm
- Top-middle section:
- Height: 3 cm
- Width: 6 cm
- Depth (same common depth): 6 cm
- Bottom-right section:
- Height: 2 cm
- Width: 6 cm
- Depth (same common depth): 6 cm
Overall length of the combined shape: 9 cm
#### Key Measurements:
The L-shaped solid is made up of three rectangular sections:
1. Left section: 4 cm x 6 cm x 6 cm
2. Top-middle section: 6 cm x 3 cm x 6 cm
3. Bottom-right section: 2 cm x 6 cm x 6 cm
The labeled measurements indicate the following:
- Height of each section in cm: 6 cm, 3 cm, 4 cm, and 2 cm.
- Combined length of sections: 9 cm.
- Common depth for each section: 6 cm.
**Goal:**
Calculate the volume of plaster needed in cubic centimeters.
#### Formula:
To find how much plaster the student needs, we'll calculate the volume of each section and sum them all up.
\[ \text{Volume (V)} = \text{Length (L)} \times \text{Width (W)} \times \text{Height (H)} \]
Let's break down the calculations:
1. Volume of the left section:
\[V_1 = 4\, \text{cm} \times 6\, \text{cm} \times 6\, \text{cm} = 144\, \text{cm}^3\]
2. Volume of the top-middle section:
\[V_2 = 6\, \text{cm} \times 3\, \text{cm} \times 6\, \text{cm} = 108\, \text{cm}^](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7f04a1a-45ee-492d-ae93-723f96ad8e53%2Fc74c6c04-eb82-4dc0-bf5c-61c05333047c%2F4rxlye_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Volume Calculation of a Composite Solid
A student is designing a rectangular solid to place in front of her model of a library. Here is the problem she is trying to solve:
#### Problem Statement:
Put in front of her model of a library. How much plaster does she need?
#### Diagram Explanation:
The shape provided is an L-shaped composite solid with the following dimensions:
- Left section:
- Height: 6 cm
- Width: 4 cm
- Depth (common for the entire figure): 6 cm
- Top-middle section:
- Height: 3 cm
- Width: 6 cm
- Depth (same common depth): 6 cm
- Bottom-right section:
- Height: 2 cm
- Width: 6 cm
- Depth (same common depth): 6 cm
Overall length of the combined shape: 9 cm
#### Key Measurements:
The L-shaped solid is made up of three rectangular sections:
1. Left section: 4 cm x 6 cm x 6 cm
2. Top-middle section: 6 cm x 3 cm x 6 cm
3. Bottom-right section: 2 cm x 6 cm x 6 cm
The labeled measurements indicate the following:
- Height of each section in cm: 6 cm, 3 cm, 4 cm, and 2 cm.
- Combined length of sections: 9 cm.
- Common depth for each section: 6 cm.
**Goal:**
Calculate the volume of plaster needed in cubic centimeters.
#### Formula:
To find how much plaster the student needs, we'll calculate the volume of each section and sum them all up.
\[ \text{Volume (V)} = \text{Length (L)} \times \text{Width (W)} \times \text{Height (H)} \]
Let's break down the calculations:
1. Volume of the left section:
\[V_1 = 4\, \text{cm} \times 6\, \text{cm} \times 6\, \text{cm} = 144\, \text{cm}^3\]
2. Volume of the top-middle section:
\[V_2 = 6\, \text{cm} \times 3\, \text{cm} \times 6\, \text{cm} = 108\, \text{cm}^
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