Amountaintop is a height y above the level ground. a woman measures the angle of elevation of the mountaintop to be θ when she is a horizontal distance x from the mountaintop. after walking a distance d closer to the mountain, she measures the angle of elevation of the mountaintop to be φ. neglecting the height of the woman’s eyes above the ground, draw a well-labelled diagram representing this situation and find an expression for the height of the mountain, y, in terms of d, φ, and θ. note that your expression cannot contain x.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)