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HELP PLEASE I'LL GIVE 25 POINTS!!! A triangular prism of cheese is measured and found to be 2.0 inches tall. The edges of its base are 9.0, 9.0, and 4.0 inches long. Several congruent prisms are to be arranged around a common 2.0- inch segment, as shown. How many prisms can be accommodated? What is their total volume? PLEASE INCLUDE WORK
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HELP PLEASE ILL GIVE 25 POINTS A triangular prism of cheese is measured and found to be 20 inches tall The edges of its base are 90 90 and 40 inches long Severa class=

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mlarsen5000

Answer:

14 prisms can be accomodated

Their total volume would be 504 in³

Step-by-step explanation:

First, we have to figure out the angle at the vertex.  For that, we need the Law of cosines. c²=a²+b²-2ab*cos(c)

4²=9²+9²-2(9)(9)cos(c)

16=81+81-162cos(c)

16-81-81=-162cos(c)

-142=-162cos(c)

-142/-162=cos(c)

.9=cos(c)

use the inverse

cos^-1(.9)=c

25.8=c

Now that we know c=25.8, we can figure out how many cheese wedges there would be in the circle.

36÷25.8=14

Now we figure out volume.

1/2(9)(4)(2)=36 in³

The total volume would be

14x36=504 in³

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