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3- What is the mass [kg] of the solid object that will be formed by rotating the y-axis of the shaded area in the figure by 110 degrees? Density p-7850kg/m3, a 30mm, b-75mm, c 45mm, d-60mm y4

3- What is the mass [kg] of the solid object that will be formed by rotating the y-axis of the shaded area in the figure by 110 degrees? Density p-7850kg/m3, a 30mm, b-75mm, c 45mm, d-60mm y4

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**Problem Statement:** ### Calculation of Mass of a Rotated 3D Shape **Question:** What is the mass [kg] of the solid object that will be formed by rotating the y-axis of the shaded area in the figure by 110 degrees? **Given Data:** - Density (\( \rho \)) = 7850 kg/m³ - \( a \) = 30 mm - \( b \) = 75 mm - \( c \) = 45 mm - \( d \) = 60 mm **Diagram Analysis:** The diagram provided is a 2D plot with the shaded area indicating a geometric region that will be rotated about the y-axis to form a 3D object. The coordinates and dimensions are labeled as follows: - \( x \) and \( y \) axes are marked. - From the origin, the x-axis is divided into two distances: \( a \) and \( b \). - The shaded area extends from \( a \) to \( b \) along the x-axis. - The height of the shaded area at distance \( a \) is \( c \). - The height of the shaded area at distance \( b \) is \( d \). The diagram likely represents a trapezoid or a triangle in the 2D plane, which, when rotated about the y-axis, forms a 3D shape (such as a conical frustum or solid of revolution). The mass calculation will involve determining the volume of the solid and then using the given density to find the mass. **Notes:** - The units must be consistent. The given dimensions in millimeters should be converted to meters for the final mass calculation. - Volume calculation involves applying the principles of solids of revolution. This problem is framed to help students understand the mathematical concepts of geometry, calculus, and physics in relation to real-world applications. Detailed steps and calculations on the Educational platform would guide learners through solving this type of problem methodically.
Transcribed Image Text:**Problem Statement:** ### Calculation of Mass of a Rotated 3D Shape **Question:** What is the mass [kg] of the solid object that will be formed by rotating the y-axis of the shaded area in the figure by 110 degrees? **Given Data:** - Density (\( \rho \)) = 7850 kg/m³ - \( a \) = 30 mm - \( b \) = 75 mm - \( c \) = 45 mm - \( d \) = 60 mm **Diagram Analysis:** The diagram provided is a 2D plot with the shaded area indicating a geometric region that will be rotated about the y-axis to form a 3D object. The coordinates and dimensions are labeled as follows: - \( x \) and \( y \) axes are marked. - From the origin, the x-axis is divided into two distances: \( a \) and \( b \). - The shaded area extends from \( a \) to \( b \) along the x-axis. - The height of the shaded area at distance \( a \) is \( c \). - The height of the shaded area at distance \( b \) is \( d \). The diagram likely represents a trapezoid or a triangle in the 2D plane, which, when rotated about the y-axis, forms a 3D shape (such as a conical frustum or solid of revolution). The mass calculation will involve determining the volume of the solid and then using the given density to find the mass. **Notes:** - The units must be consistent. The given dimensions in millimeters should be converted to meters for the final mass calculation. - Volume calculation involves applying the principles of solids of revolution. This problem is framed to help students understand the mathematical concepts of geometry, calculus, and physics in relation to real-world applications. Detailed steps and calculations on the Educational platform would guide learners through solving this type of problem methodically.
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