Bunuel wrote:
This question is from Official Guide and Official Answer is C. About rectangular solid:
In a rectangular solid,
all angles are right angles, and
opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.
Volume of rectangular solid is Volume=Length*Height*Depth.
BACK TO THE ORIGINAL QUESTION:
What is the volume of a certain rectangular solid?(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).
To elaborate more:
If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\);
If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).
Two different answer, hence not sufficient.
(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.
(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.
To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).
Answer: C.
Hope it helps.
Attachment:
800px-Cuboid.png
Sorry to bring this topic up again. I went through the discussion of this question but I'm still not satisfied with the explanation of statement 2.
Statement 2 seems a bit too ambiguous to me.
If we consider statement 1 to analyse statement 2, then the 2 opposite faces are the faces which were not included in statement 1.
If this is true, then solution above is perfect. Although it doesn't seem logical to me to consider statement 1 for analysing statement 2.
Let us not consider statement 1 at all and just focus on statement 2.
It says "each of the two opposite faces" has area 40.
There are three pairs of opposite faces. Red face and it's opposite face, blue face and it's opposite face and, yellow face and it's opposite face.
Question says each of the two opposite faces has area 40. So, each of the 6 faces must have area = 40.
Let l,b and h be the length, breadth and height respectively. Then, lb=40, bh = 40 and lh = 40.
Now,
\(lb*bh*lh = l^2b^2h^2 = 40*40*40\)
or \(l^2b^2h^2=64000\)
or \(lbh = 80\sqrt{10}\)
SUFFICIENT
Why is my solution wrong ?
Why do we have to consider constraints in statement 1 to analyse statement 2 individually ?