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= A = Bh : A = Bh :A Th %3D

= A = Bh : A = Bh :A Th %3D

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 35E
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The image appears to be a screenshot of an educational website illustrating the formulas for the volumes of various geometric shapes. ### Explanation: #### Geometric Shapes and Formulas: 1. **Rectangular Prism (illustrated in the top diagram)** - The volume formula is given by: \[ A = Bh \] - Where \( B \) is the area of the base and \( h \) is the height. 2. **Cone (illustrated in the bottom diagram)** - The volume formula is given by: \[ A = \frac{Bh}{3} \] - Where \( B \) is the area of the base and \( h \) is the height. - Alternatively, the volume of a cone can also be expressed in terms of the radius \( r \) of the base and the height \( h \) as: \[ A = \frac{\pi r^2 h}{3} \] 3. **Cylinder (not directly illustrated but included in the formulas)** - The volume formula for a cylinder is: \[ A = \pi r^2 h \] ### Summary of Formulas Displayed: - \( A = Bh \) - \( A = \frac{Bh}{3} \) - \( A = \pi r^2 h \) - \( A = \frac{\pi r^2 h}{3} \) These formulas define the volumes for different geometric shapes, serving as a quick reference for students learning about geometry.
Transcribed Image Text:The image appears to be a screenshot of an educational website illustrating the formulas for the volumes of various geometric shapes. ### Explanation: #### Geometric Shapes and Formulas: 1. **Rectangular Prism (illustrated in the top diagram)** - The volume formula is given by: \[ A = Bh \] - Where \( B \) is the area of the base and \( h \) is the height. 2. **Cone (illustrated in the bottom diagram)** - The volume formula is given by: \[ A = \frac{Bh}{3} \] - Where \( B \) is the area of the base and \( h \) is the height. - Alternatively, the volume of a cone can also be expressed in terms of the radius \( r \) of the base and the height \( h \) as: \[ A = \frac{\pi r^2 h}{3} \] 3. **Cylinder (not directly illustrated but included in the formulas)** - The volume formula for a cylinder is: \[ A = \pi r^2 h \] ### Summary of Formulas Displayed: - \( A = Bh \) - \( A = \frac{Bh}{3} \) - \( A = \pi r^2 h \) - \( A = \frac{\pi r^2 h}{3} \) These formulas define the volumes for different geometric shapes, serving as a quick reference for students learning about geometry.
The image displays four different three-dimensional geometrical shapes along with empty labels to the right of each shape. Here is a detailed description of each shape from top to bottom: 1. **Pyramid:** - **Description:** This shape is a three-dimensional polyhedron with a polygonal base and triangular faces that converge at a single point called the apex. 2. **Ellipsoid:** - **Description:** This shape is a three-dimensional surface, which resembles a stretched or squished sphere. It looks similar to an ellipse rotated about one of its principal axes. 3. **Cube:** - **Description:** This shape is a three-dimensional figure with six equal square faces. Each face meets another at a right angle, and all the edges and vertices are the same. 4. **Cone:** - **Description:** This shape is a three-dimensional figure with a circular base and a single vertex. It tapers smoothly from the base to the vertex.
Transcribed Image Text:The image displays four different three-dimensional geometrical shapes along with empty labels to the right of each shape. Here is a detailed description of each shape from top to bottom: 1. **Pyramid:** - **Description:** This shape is a three-dimensional polyhedron with a polygonal base and triangular faces that converge at a single point called the apex. 2. **Ellipsoid:** - **Description:** This shape is a three-dimensional surface, which resembles a stretched or squished sphere. It looks similar to an ellipse rotated about one of its principal axes. 3. **Cube:** - **Description:** This shape is a three-dimensional figure with six equal square faces. Each face meets another at a right angle, and all the edges and vertices are the same. 4. **Cone:** - **Description:** This shape is a three-dimensional figure with a circular base and a single vertex. It tapers smoothly from the base to the vertex.
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