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Vinvika [58]
2 years ago
7

the figure below has an volume of 108^3 in and a height of 9 in. what are the possible dimensions of the base?

Mathematics
2 answers:
Alenkinab [10]2 years ago
7 0

Area of base

  • Volume/Height
  • 108/9
  • 12in²

So possible dimensions are optionB given

  • 1/2BH
  • 1/2(4)(6(
  • 2(6)
  • 12in²

Verified

kenny6666 [7]2 years ago
6 0

<u>To find the volume of this triangular prism</u>:

  ⇒ must use the formula: V = (Area_.of_.base)*height

<u>Let's consider the information given</u>:

  • Volume: 108 in³
  • Height: 9 in

<u>Let's plug this into the equation</u>:

   V = (Area_.of_.base) * height\\108 =  (Area_.of_.base) * 9\\ (Area_.of_.base) = 12

<u>Now let's consider the area of the base formula</u>

 Area_.of_.base = \frac{1}{2}*triangle's_.base *triangle's_.height

<u>By plugging all these choices into the Area of Base's formula,</u>

  ⇒ only the <u>second choice</u> or <u>4in by 6in</u> works

     Area_.of_.base = \frac{1}{2}*triangle's_.base *triangle's_.height\\Area_.of_.base = \frac{1}{2}*4*6\\ 12 = \frac{1}{2}*4*6\\12 = 12

<u>Answer:</u> <u>Second choice</u> or <u>4in. by 6in.</u>

Hope that helps!

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