Please answer parts 1-4 and show work. Thank you so much!

Calculus AB Assignment Practice With Many Kinds of Volumes 1. Consider the region bounded by the graphs of x = y- 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 x-axis has the shape of an equilateral triangle. (Hint: Precalc review...if one side of an equilateral triangle is s, then the area of the triangle is 3-2). r 2. The base of a solid is a region bounded by the curve 7 + = 1 (an ellipse with the major 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 (x-axis) has the shape of an isosceles triangle with height equal to _ 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 xy-plane, 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