Question

Use the general slicing method to find the volume of the following solid. The solid with a semicircular base of radius 3 whose cross sections perpendicular to the base and parallel to the diameter are squares cubic units. The volume of the solid is (Type an exact answer.)

Answer 1

on [aeb ܕܐ a substitute x² value in ean a General slicing method suppose a solid objects extends from sza to x=b and cross-section of solid perpendicular to x-axy has area given by a function A. that is integrable -. Volume of solid = v= SACR).dx. & The dimensions of square are determined by length from 1 - side of semi-circle Hence length of side = 2x & volume of is the sum of area of each square times dy as semi-circle to other x² + y²=9 sc²=9-4² side. Area= (2x)² = 4x² And eqn of circle is

Area = 4(9-43) 36 - 442. Now not use general slicing method to find volume of square where a=0 & b=3 3 S Aly).dg 3 2 $(2-40404 fredy-afvet 3014).3- 40 ) 3 3 y o 19 36 6(3-0) - 4 3-03) 4 / 3 3 4 36(3) - (1889) V = 72 cubic anits 72 cubic units 73

==>The volume of the solid= 72 cubic units