### Volume Calculation of a Composite SolidA 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 cmOverall 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 cm2. Top-middle section: 6 cm x 3 cm x 6 cm3. Bottom-right section: 2 cm x 6 cm x 6 cmThe 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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Answered: put in front of her model of a library.…

Math

Algebra

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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Question

### 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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