Concrete sections for a new building have the dimensions (in meters) and shape shown in the figure. (a) Find the area of the face of the section superimposed on the rectangular coordinate system. (Round your answer to three decimal places.) m2
Concrete sections for a new building have the dimensions (in meters) and shape shown in the figure. (a) Find the area of the face of the section superimposed on the rectangular coordinate system. (Round your answer to three decimal places.) m2
Concrete sections for a new building have the dimensions (in meters) and shape shown in the figure. (a) Find the area of the face of the section superimposed on the rectangular coordinate system. (Round your answer to three decimal places.) m2
Concrete sections for a new building have the dimensions (in meters) and shape shown in the figure.
(a) Find the area of the face of the section superimposed on the rectangular coordinate system. (Round your answer to three decimal places.) m2
(b) Find the volume of concrete in one of the sections by multiplying area in part (a) by 2 meters. (Round your answer to three decimal places.) m3
(c) One cubic meter of concrete weighs 5000 pounds. Find the weight of the section. (Round your answer to the nearest whole number.) lb
Transcribed Image Text:**Concrete Sections Analysis**
Concrete sections for a new building have the dimensions (in meters) and shape shown in the figure.
The diagram depicts a 3D view of a concrete section positioned on the rectangular coordinate system. The section is a trapezoidal prism with the following dimensions: the base of the trapezoid extends from \((-5.5, 0)\) to \((5.5, 0)\), and the height of the trapezoid measures up to 2 meters on the y-axis.
Two functions define the edges of the trapezoid:
- \(y = \frac{1}{3}\sqrt{5 + x}\) for the left edge.
- \(y = \frac{1}{3}\sqrt{5 - x}\) for the right edge.
The section extends 2 meters along the z-axis from the face plane.
**Tasks:**
(a) **Calculate the Area:**
Find the area of the face of the section superimposed on the rectangular coordinate system. (Round your answer to three decimal places.)
\[ \_\_\_\_\_\_\_ \, \text{m}^2 \]
(b) **Calculate the Volume:**
Find the volume of concrete in one of the sections by multiplying the area in part (a) by 2 meters. (Round your answer to three decimal places.)
\[ \_\_\_\_\_\_\_ \, \text{m}^3 \]
(c) **Calculate the Weight:**
One cubic meter of concrete weighs 5000 pounds. Find the weight of the section. (Round your answer to the nearest whole number.)
\[ \_\_\_\_\_\_\_ \, \text{lb} \]
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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![**Concrete Sections Analysis**
Concrete sections for a new building have the dimensions (in meters) and shape shown in the figure.
The diagram depicts a 3D view of a concrete section positioned on the rectangular coordinate system. The section is a trapezoidal prism with the following dimensions: the base of the trapezoid extends from \((-5.5, 0)\) to \((5.5, 0)\), and the height of the trapezoid measures up to 2 meters on the y-axis.
Two functions define the edges of the trapezoid:
- \(y = \frac{1}{3}\sqrt{5 + x}\) for the left edge.
- \(y = \frac{1}{3}\sqrt{5 - x}\) for the right edge.
The section extends 2 meters along the z-axis from the face plane.
**Tasks:**
(a) **Calculate the Area:**
Find the area of the face of the section superimposed on the rectangular coordinate system. (Round your answer to three decimal places.)
\[ \_\_\_\_\_\_\_ \, \text{m}^2 \]
(b) **Calculate the Volume:**
Find the volume of concrete in one of the sections by multiplying the area in part (a) by 2 meters. (Round your answer to three decimal places.)
\[ \_\_\_\_\_\_\_ \, \text{m}^3 \]
(c) **Calculate the Weight:**
One cubic meter of concrete weighs 5000 pounds. Find the weight of the section. (Round your answer to the nearest whole number.)
\[ \_\_\_\_\_\_\_ \, \text{lb} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf2a9245-87db-4e54-b147-768ccba693e7%2F4d2b3268-ed56-4080-a95b-723edac0234f%2Fsjyee8k_processed.png&w=3840&q=75)
