A solid has the following properties. When illuminated by rays parallel to the z-axis, its shadow is a circular disk. If the rays are parallel to the y-axis, its shadow is a square. If the rays are parallel to the x-axis, its shadow is an isosceles triangle. Assume that the projection onto the xz plane is a square whose sides have length 1. a) What is the volume of the largest such solid? b) Is there a smallest such volume? Explain.

The base of a garden tent is a square with side length c feet. Two semi-circular poles run between pairs of opposite vertices of the base and support the tent. Cross-sections parallel to the base are squares. Compute the volume enclosed by the tent as follows: (a) Establish a rectangular coordinate system with its origin at the center of the tent’s base, the positive y-axis pointing directly upward through the tent’s apex, and the postive x-axis passing through a vertex of the base. Sketch the tent with this coordinate system. Label the axes with their variable names and units. (b) Sketch the cross-section of the tent cut out by the xy-plane (a semi-circle) in the xy-coordinate system. Label the coordinates of the intercepts of the semi-circle. Label the axes with their variable names and units. (c) Sketch a general horizontal segment with its endpoints P and Q on the semicircle in part (b). Label the coordinates of its endpoints P and Q as (−x, y) and (x, y), respectively. Assume x…

Find the volume of the indicated region.the region bounded above by the sphere x2+y2+z2=36   and below by the cone z=square root of x2+y2  . Using Spherical coordinate may simplify the computation. Here another way to express the cone will be φ = pi/4 . We did very similar problem in the class.   a) 72π(2 -square root of 3 )   b) 54π(2 - square root of 3)   c) 54π(2 - square root of 2 )   d) 72π(2 - square root of 2)

3. If G is the centroid of AACE, AG = 8, GF' = 7, and BG = 5, find each missing measure. a) GD =. b) AD = B. c) CG = d) GE = E e) BE =