Geometry Problems.

[Obsession]

We recieved this word problem in class:

Rufus Leaking stores his collection of cannonballs in cubical boxes that have no tops.

~The volume of each box equals its surface area (Units are in cubic feet)
~The volume of each cannonbal equals its surface area. (Units are in cubic inches)

How many cannonballs can Rufus fit into each box?

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I first found the side of the cube, 6, and then found the volume and surface area, 216 ft^3.

Then I found the colume of each cannonball, 36. The radius is 3 in this case.

I multiplied the volume of the cube to get inches.
216 * 12 = 2592
Then divided that by 36 = 2595/36 to get 72.
Which would mean that he could fit 72 cannonballs in one box.

Is this correct, because it doesn't seem like it. Did I miss a step?

 

[soroban]

Hello, Obsession!

Rufus Leaking stores his collection of cannonballs in cubical boxes that have no tops.

The volume of each box equals its surface area. .(Units are in feet.)
The volume of each cannonbal equals its surface area. .(Units are in inches.)

How many cannonballs can Rufus fit into each box?

You started correctly . . .

The side of the box is \(\displaystyle 6\text{ ft }\:=\:72\text{ inches.}\)
. . Its volume is: \(\displaystyle \:72^3\:=\:373,248\text{ in}^3\)

The radius of a cannonball is \(\displaystyle 3\text{ inches.}\)
. . Its volume is: \(\displaystyle \:\frac{4}{3}\pi\cdot 3^3\:=\:36\pi\text{ in}^3\)

Then: \(\displaystyle \:373,248\,\div\,36\pi\:=\:3300.2369\)

Answer: \(\displaystyle \,3300\) cannonballs per box.

 

[Obsession]

omg..... I Can't believe I didn't convert to inches BEFORE cubing! And I also missed cubing the radius...

Sometimes I wonder about myself.....

I'm so sorry for any confusion I may have caused

-10 points for jwpaine

I did the same thing...plus I forgot to add [pi] back on.

 

[Obsession]

Another problem...

I just need a little more help:

Lester Turlbutt has packed spheres that are one-unit in diameter into a rectangular tray, filling the tray in a single layer with no slack, using a rectangular packing. But Lester wantes tp add more spheres. First he tries a different arrangement that allows him to add one sphere. But then, using a third arrangement, he finds that he is able to fit in still another sphere. What are the dimensions of the tray?


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I don't know how to start this problem.