anonymous
  • anonymous
The volume of a regular triangular prism is 90 sqrt of 3 cm^3. If the radius of the inscribed circle in the base is 3 cm, find the altitude of the prism.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Do you remember the equation for the volume of the prism?
anonymous
  • anonymous
V = Bh
anonymous
  • anonymous
or we could use V = Re

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anonymous
  • anonymous
And I draw that wrong. Let me redo.
anonymous
  • anonymous
Ok the base is a regular triangle with inscribed circle of 3cm, kinda like:|dw:1370256108076:dw| Every side of the triangle measures a
anonymous
  • anonymous
Forgive the circle. It should touch the triangle on the 3 sides.
anonymous
  • anonymous
It's tangent right?
anonymous
  • anonymous
I mean the circle is tangent to the triangle.
anonymous
  • anonymous
yes the circle is tangent to all sides of the triangle. Do you think you can solve the sides?
anonymous
  • anonymous
Wait, I don't get it. If the radius of the circle is 3cm, then all of the sides of the triangle are also 3 cm? Because that is what you said on your drawing.
anonymous
  • anonymous
|dw:1370256522089:dw| Looks a little off too. But gives the right idea. No. The sides don't measure 3cm, they are much larger or else the triangle would fit inside the circle.
anonymous
  • anonymous
What is the angle on a regular triangle? It is 60° right?
anonymous
  • anonymous
That is an equilateral triangle - 60 degrees
anonymous
  • anonymous
The base of a regular prism is a regular polygon, for a triangle that is an equilateral triangle. So we are going the right track here.
anonymous
  • anonymous
Can you find out how much does the segment AD measures? |dw:1370257102289:dw|
anonymous
  • anonymous
AD = cotg(30°) \(\times\) 3cm = \(\sqrt{3}\times 3\)
anonymous
  • anonymous
I got 264. 27
anonymous
  • anonymous
You got 264.27 for the final answer of the prisms height?
anonymous
  • anonymous
No. for the AD.
anonymous
  • anonymous
The final answer I got for the height is 3.3333. But AD is not that. Can you indicate on the drawing how you calculated?
anonymous
  • anonymous
|dw:1370259595698:dw| \[\frac{\overline{CD}}{\overline{AD}}=\tan(30°)\\ \frac{\overline{CD}}{\overline{AD}}=\frac{\sqrt{3}}{3}\\ {\overline{AD}}=\sqrt{3}\quad\overline{CD} \]

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