# WitCH 132: You’re Soaking In It

This the last one from the 2017 Year 7 test, again from the calculator part.

## 14 Replies to “WitCH 132: You’re Soaking In It”

1. Mark says:

The diagonal of the marble cube is nearly 104cm, meaning it couldn’t necessarily fit inside the solid acrylic prism… well, not on all angles.

1. marty says:

That’s very funny. I hadn’t even thought of that. But I think you’re right. If the cube is placed as suggested by the picture, with the top vertex directly above the bottom vertex, then I don’t think the cube can fit (even if rotated around the vertical axis).

1. Back in Black says:

And nary a “not to scale” to be seen.

(“I canna’ change the laws of physics, Captain!” Whispers – “But I can change the laws of mathematics.”)

2. marty says:

Yep, it won’t fit, even if the cube is rotated about the vertical axis. It comes down to trying to fit a regular hexagon in a square, and in this case the hexagon is too big. I did some quick and unchecked computations, and Burkard agreed.

1. J.D. says:

I could very well be wrong, but the picture doesn’t suggest to me that one vertex is placed directly above the opposite one. It appears to me as though the lowest vertex is closer to us than the highest one is, and the lowest vertex is not in contact with the base of the prism.

1. marty says:

Thanks, J.D. Absurdity is in the eye of the beholder.

It doesn’t matter of course. The question is plain silly whether or not the cube fits. Why not just dunk the damn thing in a fish tank?

But, accepting that their drawings are so bad that anything might be true, it still looks to me to be pretty vertical. Comparing the top and bottom vertices to the top and bottom faces, both vertices look pretty middlish to me.

2. Red Five says:

But this is Napland, the rules of measurement only apply when the wizard says they do.

3. ThatGuy says:

I read, “Jenny is making a cake,” I say (to myself or out loud), “No she’s not.”
Easy fun game. Can’t recommend it highly enough.
Out of interest, the sculpture would weigh more than a ton, and the block of marble therein would be worth thousands.
Good on ya Josie.

1. marty says:

Very funny!

1. Libby says:

You’d need some big machinery to suspend a ton of marble while the acrylic sets, but of course the marble in question won’t fit anyway, being significantly larger and heavier than a frog, but then I’m going off on a tangent

2. Back in Black says:

I’m wondering how Josie is able to be inside a solid acrylic prism (crouching, I assume) to make the sculpture of the marble cube and what’s happened to the excess marble that’s been carved off.

1. Back in Black says:

Thank you, ThatGuy. Now I see how Jose did it – they wore scuba gear (as a Frogman would) and completed the sculpture before the acrylic set. They must have collected the excess marble in a sealed bag and topped up the acrylic when they climbed out.

I think this question would be much better suited in the NAPLAN Narrative Writing Task. Perhaps the questions got mixed up.

4. Libby says:

Just out of curiosity, how did the marble cube get inside the prism? We’re the acrylic pieces just glued to the outside? It can’t be cut from the inside out???

1. ThatGuy says:

You can make up acrylic as a liquid, then wait, and it sets into a hard plastic. Kinda like putting chocolate frogs in a dish, pouring in liquid jelly, and a couple of hours later, chocolate frogs embedded in a solid (solid?). Hmmmmmm, frogs in jelly. I’ll be back in a couple of hours.