What is the volume of the truncated solid if each base is 36 and each lateral edge is 12 sq.rt. 21.

A truncated pyramid is what is left when a plane parallel to the base cuts off the top. If a regular hexagon pyramid is truncated half way from the base to the top, what is the volume of the truncated solid if each base edge is 36 and each lateral edge is 12 sq.rt. 21?

What percent of the rectangular prism is outside of the triangular prism.

AEF is a triangle , ABCD is a rectangle AB = 6 AE= 10 AD = 11 EF = 5 AF = 5 sq.rt. 5 The attached picture is the base of a right prism - a triangular prism inside of a rectangular prism. Both prisms are 20 in height. What percent of the rectangular prism is outside of the triangular prism.

Cycloid Geometry

The circle has a radius of 8. As the circle rolls along the line, the point P (a pencil point) draws a curve. a) Draw the curve for three complete revolutions of the circle. b) Find the area between the curve (one loop) and the line. c) Find the length of the curve - all three loops.

the attached rolling circle

Here the rolling circle is rolling along inside and tangent to a fixed circle. a) Draw the curve which is traced by P as the rolling circle goes all of the way around the inside of the fixed circle. Assume R=3r. c) Determine the related curves under these conditions: 1)Epicycloid with R=r 2)Epicycloid with R=2r 3) Epicycloid with R=3r Can you make a conjecture about the epicycloid if R=nr? 4) Hypocycloid with R=2r 5)Hypocycloid with R=4r Can you make a conjecture abaout the hypocycloid if R=nr?

Brachistrochrome Problem

What is it's origin? State the problem with picture Explain how the cycloid relates to the solution.