A
B
C
D
E
Let LW = 72 such that L=6 and W=12.M7MBA wrote:If a rectangular box has two faces with an area of 30, two faces of area 60, and two faces of area 72, what is its volume?
A. 60
B. 90
C. 162
D. 300
E. 360
Hello M7MBA.M7MBA wrote:If a rectangular box has two faces with an area of 30, two faces of area 60, and two faces of area 72, what is its volume?
A. 60
B. 90
C. 162
D. 300
E. 360
The OA is E.
Should I set a system of 3 equations here? Or, what should I do? I'd appreciate some help.
Nice approach.Vincen wrote:Hello M7MBA.
Here is a fast way to solve this PS question.
We know the following: $$\left(1\right)\ \ \ \ W\cdot L=30$$ $$\left(2\right)\ \ \ \ W\cdot H=60$$ $$\left(3\right)\ \ \ \ L\cdot H=72$$ Now, let's calculate the volumen squared, that is to say, $$V^2=\left(W\cdot L\cdot H\right)^2=W\cdot W\cdot L\cdot L\cdot H\cdot H$$ $$=\left(W\cdot H\right)\cdot\left(W\cdot L\right)\cdot\left(L\cdot H\right)$$ $$=\left(60\right)\cdot\left(30\right)\cdot\left(72\right)$$ $$=129600.$$ $$\Rightarrow\ \ \ V=\sqrt{129600}$$ $$\Rightarrow\ \ \ V=360.$$ Therefore, the correct answer is the option E.
Since the volume of a box is V = l x w x h and the area of one of its face is the product of two of the three dimensions, we can assume that l x w = 30, l x h = 60 and w x h = 72. From the three equations, we can see that the only numbers that satisfy them are 5, 6 and 12. That is, 5 x 6 = 30, 5 x 12 = 60 and 6 x 12 = 72. Therefore, the volume of the box is V = 5 x 6 x 12 = 360.M7MBA wrote:If a rectangular box has two faces with an area of 30, two faces of area 60, and two faces of area 72, what is its volume?
A. 60
B. 90
C. 162
D. 300
E. 360
