1. Consider the region bounded by the graphs of x : y2 and x : 9. Find the volume of the solid that has this region as its base if every cross section by a plane perpendicular to the xaxis has the shape of an equilateral triangle. (Hint: Precalc review...if one side of an equilateral triangle 32) 4 . is s, then the area of the triangle is 2 2. The base of a solid is a region bounded by the curve i + y : 1 (an ellipse with the major 82 42 and minor axes of lengths 16 and 8 respectively). Find the volume of the solid if every cross section by a plane perpendicular to the major axis (xaxis) has the shape of an isosceles triangle with height equal to 11 the length of the base. Calculus AB Assignment Practice With Many Kinds of Volumes 3. The base of a solid is a right triangle whose base side has length a and whose perpendicular side has length %a. Find the volume of the solid if cross sections perpendicular to the base of the triangle are semicircles. 4. A solid has as its base the region bounded by the curves y = 2x2 +2 and y = x2 +1. Find the volume of the solid if every cross section of a plane perpendicular to the x-axis is a trapezoid with lower base in the Jayplane, upper base equal to % the length of the lower base, and height equal to 2 times the length of the lower base. Brain Teaser: A tetrahedron has three mutually perpendicular faces and three mutually perpendicular edges of lengths 2, 3, and 4 cm, respectively. Find its volume