Calculus
Answers
(a) Volume of the solid with square cross-sections To find the volume of the solid with cross-sections perpendicular to the x-axis being squares, let us consider the area of squares at a particular x value. From the graph, we can observe that at x = 0, the height of the square cross-section will be 0. And for x = 2, the height will be 4. Thus, the area of a square at any x value from 0 to 2 will be the square of the corresponding y-value i.e. (y = x^2). Hence, using the formula for calculation of volume of solid of revolution (formed when a function is revolved around an axis), we can express the volume of the required solid as V = ∫x2*(x^2)dx from 0 to 2 V = ∫x^4 dx from 0 to 2 V = (1/5)x^5 from 0 to 2 V = (1/5)*2^5 V = 16/5 Hence, the volume of solid with square cross-sections is 16/5. (b) Volume of the solid with semicircle cross-sections To find the volume of solid with semicircle cross-sections perpendicular to the x-axis, let us consider the area of semicircles at a particular x value. From the graph, we
