Radius of Gyration of an Area Learning Goal: To understand how to calculate the area, moment of inertia, and radius of gyration for various shapes. The radius of gyration of an area about an axis is a quantity that is often used for the design of columns in structural mechanics. Once the areas and moments of inertia are known, the radii of gyration are determined using the formulas kx and ky where the moments of inertia are calculated using the formulas Ix=14² dA and I, 4x² dA. Part A - The Radii of Gyration for a Cubic Function The figure shows an area bounded by the positive x axis, the vertical line x = L, and the function y For L = 3.4 ft, calculate the radius of gyration about x, k, and the radius of gyration about y, k, for this area. L Express your answers, separated by commas, to three significant figures. You did not open hints for this part. ANSWER: kx-, ky= ft, ft = -x L Part B - The Radii of Gyration for a Non-Polynomial Function The figure shows an area bounded by the positive x axis, the vertical line x = b, and the function 2 = 13. For b = 2.90 m, calculate the radius of gyration about x, k, and the radius of gyration about y, ky, for this area. Express your answers, separated by commas, to three significant figures. h You did not open hints for this part. ANSWER: = kx-, ky m, m y² = x³ Part C - The Radii of Gyration for a Triangle h The figure shows a triangle bounded by the positive x axis, the positive y axis, and the line y = *(b-x). For b 1.75 ft and h = 2.75 ft, calculate the radius of gyration about.x, k and the radius of gyration about y, k, for this triangle. Express your answers, separated by commas, to three significant figures. You did not open hints for this part. ANSWER: = ft, ft h y=h(b-x)/b b -x b x