Question

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

Answer 1

Area of base

• Volume/Height
• 108/9
• 12in²

So possible dimensions are optionB given

• 1/2BH
• 1/2(4)(6(
• 2(6)
• 12in²

Verified

Answer 2

To find the volume of this triangular prism:

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

Let's consider the information given:

• Volume: 108 in³
• Height: 9 in

Let's plug this into the equation:

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

Now let's consider the area of the base formula

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

By plugging all these choices into the Area of Base's formula,

  ⇒ only the second choice or 4in by 6in works

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

Answer: Second choice or 4in. by 6in.

Hope that helps!