fskilnik wrote:
The water tank shown is a prism with 3 rectangular faces and 2 equilateral triangular faces. Each triangular face has height 6, and the water surface is parallel to the face ABCD. If the volume occupied by the water is half the volume of the water tank, which of the following is closest to the length of x ?
(A) 1.73
(B) 2.83
(C) 3.46
(D) 4.24
(E) 5.20
GMATH practice exercise (Quant Class 17)
Very good, Mahmoudfawzy83 ! Congrats (kudos!) and thank you for your contribution!
Let me offer our "official solution": (It is only different of yours in the "wording".)
\(?\,\, \cong \,\,x\)
\(\frac{1}{2}\,\, = \,\,\frac{{{V_{{\text{water}}}}}}{{{V_{{\text{tank}}}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{{S_{\Delta EFG}} \cdot FH}}{{{S_{\Delta EAD}} \cdot DC}}\,\,\,\mathop = \limits^{FH = DC} \,\,\,\frac{{{S_{\Delta EFG}}}}{{{S_{\Delta EAD}}}}\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,{\left( {\frac{x}{6}} \right)^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\frac{x}{6} = \frac{{\sqrt 2 }}{2}\)
\(\left( * \right)\,\,{\text{formula}}\,\,{\text{given}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {**} \right)\,\,{\text{similarity}}\,\,{\text{property}}\)
\(? = x\,\, = \,\,3\sqrt 2 \,\, \cong \,\,3 \cdot 1.41 = 4.23\)
The correct answer is therefore (D).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.