The New Face ^_^

Geometry Level 1

The three faces of a rectangular box have areas of $40$ , $45$ , and $72$ square inches. What is the volume, in cubic inches, of the box?

Try this one .

300

330

450

360

3 solutions

Rishabh Tripathi
Mar 25, 2015

Let $\text{Lenght}=l , \text{Breadth}=b , \text{Height}=h$

According to question

$lb=45$

$lh=72$

$bh=40$

Multiply all the equations

So, $l^{2}b^{2}h^{2}=45 \times 72 \times 40$

$\text{Volume}= lbh= \sqrt{45 \times 72 \times 40}$

$\text{Volume}=\boxed{360}$

Vasudev Chandna
Mar 25, 2015

Let the sides of the cuboid be A, B and C

Given that-

AB=40

BC=45

AC=72

Then,

A/C=8/9-----(1)

A/B=8/5-----(2)

B/C=5/9-----(3)

Now, after adding all the equations, we will get B=5

Put this value in the given areas to get other sides.

If anybody wants the solution on how to add the equations, please comment!

Note that the volume of the box is simply $ABC$ and hence we don't need to find $A,B,C$ individually. Simply multiply all the three equations.

$\begin{cases}AB=40\\ BC=45\\ CA=72\end{cases}\implies (ABC)^2=40\times 45\times 72=(\pm 360)^2\implies ABC=360$

We reject $ABC=(-360)$ since volume cannot be negative.

Prasun Biswas - 6 years, 2 months ago

Lol, yeahh My method would have worked if they asked for the lengths of the sides.

Vasudev Chandna - 6 years, 2 months ago

The dimensions are actually $9,8,5$ which is pretty much trivial if one uses a number theoretical approach.

Prasun Biswas - 6 years, 2 months ago

By the way, I'm kinda new. I wanted to ask you that when I point my cursor at your solution, it shows a coding. I've seen this many times.

So do you know programming?

Vasudev Chandna - 6 years, 2 months ago

That is actually the $\LaTeX$ typesetting users use here to type math equations. You can read more about it in the "Formatting Guide" at the bottom left corner of your comment box.

Prasun Biswas - 6 years, 2 months ago

@Prasun Biswas – Woah, that's awesome! I thought this place was full of programmers. xD

Vasudev Chandna - 6 years, 2 months ago

@Vasudev Chandna – Nope, but there are still some elite programmers here in our community.

Prasun Biswas - 6 years, 2 months ago

Raylin Panes
Apr 4, 2015

Let A.B and C be the sides of cube/cuboid AB=40 BC=45 AC=72 >> (360)^2 and positive no sides are negative

The New Face ^_^

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