Find the Volume, Surface Area, and Lateral Surface Area of the pyramids and cone. If someone could include their work and how they got their answer that would be great! Thanks.

http://i4.photobucket.com/albums/y10...s/problems.jpg

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- Apr 14th 2008, 03:29 PMpeachgalVolume, Surface Area, and Lateral Surface Area
Find the Volume, Surface Area, and Lateral Surface Area of the pyramids and cone. If someone could include their work and how they got their answer that would be great! Thanks.

http://i4.photobucket.com/albums/y10...s/problems.jpg - Apr 15th 2008, 12:40 AMearboth
Let denote the base area, the lateral surface area and H the height of the solid.

Then the volume is calculated by:

to #a.: a_B is a rectangle (84) and the height is 19. Thus

to #b.: Let s denote the side of the hexagon. Then

Now use the general formula to calculate the volume.

to #c.: All areas are half rectangles. So I'm sure that you can do the calculations.

to #d.: is a circle with . Use the general formula to calculate the volume ( )

To calculate the surface area or the lateral surface area is a little bit more tricky. If the solid is a right solid and the base area is a regular polygon or a circle then the lateral surface consists of congruent triangles or a sector of a circle. In this case the lateral surface is calculated by:

. This formula can be used at #b. and #d.. In both cases you must calculate the height h of the triangle first.

to #a.: The lateral surface area consists of 4 right triangles.

The complete surface area consists of

to #d. Let s denote the line segment from the tip of the cone to the edge of the base area then

. The complete surface area is:

to #c.: All areas are right triangles (that means half rectangles) and I'm sure that you can do the calculations. Post your results so we can check.