Question

I AM CALLING ALL ACES, EXPERTS, SMARTY PANTS, ETC!!! :)) (MATH 50 POINTS)

10. The base of a triangular prism is a triangle with a base of 4 inches and a height of 3.5 inches. The height of the triangular prism is 3.3 inches. What is the volume of the triangular prism?
The volume of the triangular prism is 23.1.




11. The base of a triangular pyramid is a triangle with a base of 4 inches and a height of 3.5 inches. The height of the triangular pyramid is 3.3 inches. What is the volume of the triangular pyramid?





12. What do the triangular pyramid and prism in items 10 and 11 have in common? How are their volumes related?





13. Write in symbols how the volume of the triangular pyramid relates to the volume of the triangular prism. Use y for the volume of the pyramid and r for the volume of the prism. Explain what the symbols mean in words.

Answer 1

10. The volume of the triangular prism is
`V=A_(base)\cdot H=(1)/(2) height \cdot base\cdot H`, then

`V=(1)/(2) \cdot 4\cdot 3.5\cdot 3.3=23.1`.

11. The volume of the triangular pyramid is
`V=(1)/(3)A_(base)\cdot H=(1)/(3)\cdot (1)/(2) height \cdot base\cdot H`, then

`V=(1)/(3)\cdot (1)/(2) \cdot 4\cdot 3.5\cdot 3.3=7.7`.

12. They have common base (common triangle). y=7.7, r=23.1, then r:y=23.1:7.7=3.

13. See 10 and 11 for notations in symbols.