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grandymaker [24]
3 years ago
13

n the right triangular prism below, BG FC The volume of the prism is 900 cubic centimeters. The height of the prism is 15 centim

eters and the height of the triangular base is 10 centimeters. What is the length of edge FC?
Mathematics
2 answers:
Fofino [41]3 years ago
7 0

Answer:

12 cm

Step-by-step explanation:

Bad White [126]3 years ago
6 0
12 cm

Remember, V=Bh

-I think I did the process incorrectly but this is what I did:
900=(10)(15)
900=150 (divide 150 on both sides)
you get 6 but then I multiplied by 2 and got 12.
The answer 12 is correct though so I hope this helped! and if someone could explain the process better that would be great lol.
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\bf \textit{volume of a rectangular prism}\\\\&#10;V=lwh\quad &#10;\begin{cases}&#10;l = length\\&#10;w=width\\&#10;h=height\\&#10;-----\\&#10;w=l=x&#10;\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\&#10;-------------------------------\\\\&#10;\textit{surface area}\\\\&#10;S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h&#10;\\\\\\&#10;\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\&#10;-------------------------------\\\\&#10;V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3

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now, let's check if it's a maximum point at 10, by doing a first-derivative test on it.  Check the second picture below.

so, the volume will then be at   \bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3

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