The base of a three-dimensional figure is bound by the circle x² + y² = 9. Vertical cross sections that are perpendicular to the y-axis are isosceles triangles with height equal to 3. Algebraically, find the area of each triangle. 54- O A(Y) = O A(y) = 3 V 9 O A(Y) = 2 19-y² O A(y) = √√√9-y²

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**Finding the Area of Cross-Sectional Triangles in a Three-Dimensional Figure**

**Problem Statement:**
The base of a three-dimensional figure is bound by the circle \(x^2 + y^2 = 9\). Vertical cross-sections that are perpendicular to the y-axis are isosceles triangles with height equal to 3.

**Objective:**
Algebraically find the area of each triangle.

**Illustration:**
There is a diagram showing a circle on the \(xy\)-plane with the equation \(x^2 + y^2 = 9\). The circle is centered at the origin (0,0) with a radius of 3. The area within this circle is shaded.

**Graphical Details:**
The y-axis is labeled from -5 to 5, and the x-axis is labeled from -5 to 5. The circle intersects these axes at \(x = 3, x = -3, y = 3,\) and \(y = -3\).

Formatted as a multiple-choice question, the problem presents the following options for the area \(A(y)\) of each triangle:

1. \(A(y) = \sqrt{9 - y^2}\)
2. \(A(y) = 3\sqrt{9 - y^2}\)
3. \(A(y) = 2\sqrt{9 - y^2}\)
4. \(A(y) = \frac{1}{2} \sqrt{9 - y^2}\)

The solution involves choosing the correct mathematical expression for the area of the isosceles triangles.
Transcribed Image Text:**Finding the Area of Cross-Sectional Triangles in a Three-Dimensional Figure** **Problem Statement:** The base of a three-dimensional figure is bound by the circle \(x^2 + y^2 = 9\). Vertical cross-sections that are perpendicular to the y-axis are isosceles triangles with height equal to 3. **Objective:** Algebraically find the area of each triangle. **Illustration:** There is a diagram showing a circle on the \(xy\)-plane with the equation \(x^2 + y^2 = 9\). The circle is centered at the origin (0,0) with a radius of 3. The area within this circle is shaded. **Graphical Details:** The y-axis is labeled from -5 to 5, and the x-axis is labeled from -5 to 5. The circle intersects these axes at \(x = 3, x = -3, y = 3,\) and \(y = -3\). Formatted as a multiple-choice question, the problem presents the following options for the area \(A(y)\) of each triangle: 1. \(A(y) = \sqrt{9 - y^2}\) 2. \(A(y) = 3\sqrt{9 - y^2}\) 3. \(A(y) = 2\sqrt{9 - y^2}\) 4. \(A(y) = \frac{1}{2} \sqrt{9 - y^2}\) The solution involves choosing the correct mathematical expression for the area of the isosceles triangles.
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