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A building has the dimensions shown in the figure and a volume of 3840 cubic meters. How tall are the ceilings in the part of the building that is only a rectangular prism? 
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A building has the dimensions shown in the figure and a volume of 3840 cubic meters How tall are the ceilings in the part of the building that is only a rectang class=

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prestonshelton
Hello!

First you have to find the volume of the triangular prism

To find this you use the equation

[tex]V = \frac{1}{4} \sqrt{-a^{4} + (ab)^2 + 2(ac)^2 - b^4 + 2(bc)^2 - c^4 } [/tex]

h is height
a, b and c are the side lengths of the triangle

To find the side lengths you use the Pythagorean Theorem

The side lengths are about 7.2

The you put this into the equation to find the volume of a triangular prism

When you do this you get around 95.52

Subtract this from the total volume

3840 - 95.52 = 3744.48

Put this into the equation to find the volume of a rectangular prism

12 * 30 * x = 3744.48

Divide both sides by 12

30 * x = 312.04

Divide both sides by 30

x = 10.401

The answer is 10.401 meters

Hope this helps!
rams58

Answer:

10

Step-by-step explanation:

First, you want to know the volume for the triangular prism.

1. 4 * 12 * 10 = 480

2. 480 / 2 = 240

Then you subtract to find the volume only for the rectangular prism.

1. 3840 - 240 = 3600

Finally, you solve for the height

1.  12 * 30 * h = 3840

2. 360h = 3840

3. h = ~10~

The height is about 10.

Hope this helps!!

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