An oblique prism is created using rhombuses with edge lengths of 25 units. The area of one rhombus is 600 sq units. The perpendi
cular distance between the bases is 24 units. What is the volume of the prism?
2 answers:
Check the picture below.
let's recall Cavalieri's principle, that solids with equal altitudes and identitical cross-sectional areas at each part all the way up, have the same volume.
so, for a prism like this that is not oblique, with rhombic bases of area 600 and a height/altitude of 24, the volume will simply be the base * height, 600 * 24 = 14400.
well, based on Cavalieri's principle, an oblique one will also have the same volume.
Answer:
The volume of the prism is 14400 units³.
Step-by-step explanation:
It is given that an oblique prism is created using rhombuses with edge lengths of 25 units.
The volume of a prism is
..... (1)
Where, B is base area and h is height of the prism.
It is given that the area of one rhombus is 600 sq units. The perpendicular distance between the bases is 24 units.
Substitute B=600 and h=24 in equation (1) to find the volume of the prism.
Therefore the volume of the prism is 14400 units³.
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