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Question 893662: I have geometry problem that I'm stumped on! There is a rectangular prism that looks like an upright tower with a rectangular pyramid on top of it. The measurements of the prism is height 4,side 1.5, then the pyramid on top has measure base 1.5, height 2,find the volume?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if it's a rectangular prism, then it needs to have a height and a length and a width.
similarly, the rectangular pyramid on the top would need to have a base that has a length and a width equal to the length and the width of the rectangular prism that is it sitting on.
if you meant a square prism, than the length and the width would both be the same which i can then assume is equal to 1.5
i'll assume a square prism and a square pyramid on top and we'll see how to go about solving this.
the volume of the square prism is equal to the area of the base times the height.
the area of the base is equal to 1.5^2 which is equal to 2.25.
multiply that by the height and the volume of the prism is 2.25 * 4 = 9 cub9ic units.
the volume of the square pyramid is equal to 1/3 * the height * the area of the base.
the area of the base is equal to 2.25 (same as the area of the base of the prism).
the height of the pyramid is equal to 2.
the volume of the pyramid is equal to 1/3 * height * area of the base which is equal to 1/3 * 2 * 2.25 which is equal to 1.5
the total volume of the figure is therefore equal to 9 plus 1.5 = 10.5 cubic units.
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