comparing and contrasting the volumes and surface area of prisms, pyramids,cones and cylinders

The formula for finding volumes in prisms and pyramids are very similar they formulas are V=B x h for the prism and V=1/3B x h for the pyramid they are similar like this because both have bases that are polygons but the pyramid is 1/3 the volume of a prism with the same size base. 

The formulas for the cylinder and cone are also similar in this way, the cylinders formula is: V=pi x radius squared x hieght and the formula for a cone is: V= 1/3 pi r squared x h. in this the cones are also 1/3 the volume of a cylinder with the same size base.

The formulas for the surface areas differ because the lateral area formula for a pyramid is LA=1/2Perimeter slant height but the formula for a prism is LA=Perimeter slant height.

The area formula for rectangles and parallelograms are the same because a rectangle is a parallelogram.


The dimensions of tennessee are 110 north to south and 430 east to west.


The estimated area of tennessee with these dimensions is 47,300 miles squared


the actual area is 42,144 square miles

what i have learned from chapter 10

In chapter 10 i have learned how to find the circumference, diameter (2r), radius (1/2d) and the values of different kinds of angles and arcs in and on a circle. Including how to find the measures of arcs that intercept and inscribed angle which would be the measure of the angle multiplied by 2. Also one of the harder things i learned was the secant theorems which show you how to find the measures of intersecting secants, intersecting secants and tangents, and secants and tangents that intersect outside of the circle. 




one question i have about this is:
        Is the tangent we use in this chapter tied to the tangent we use in SOH CAH TOA?