The diagram shows a cube of side length 4 inches. A is a vertex of the cube, while B and C are located on opposite edges of the cube with both B and C being 1 inch from the nearest vertex.

If a plane including the points A, B, and C cuts through the cube, what is the shape of the resulting cross section?

an isosceles triangle
a rectangle
a square
a rhombus
a hexagon

Question

The diagram shows a cube of side length 4 inches. A is a vertex of the cube, while B and C are located on opposite edges of the cube with both B and C being 1 inch from the nearest vertex.

If a plane including the points A, B, and C cuts through the cube, what is the shape of the resulting cross section?

an isosceles triangle
a rectangle
a square
a rhombus
a hexagon

anonymous · Answer

attachment

anonymous · Answer

@iGreen Excuse me for bombarding you with questions, but would you mind helping me with 3 more?

igreen · Answer

Nope, I don't mind at all (:

anonymous · Answer

Thanks. I selected square for this one, but I believe i'm wrong.

igreen · Answer

Hmm.this is kind of trickly, hold on.

igreen · Answer

*tricky

anonymous · Answer

OK I don't mind waiting.

igreen · Answer

Hmm..I don't know..I seem to come up with an irregular shape.

One of the points is on the vertex..and the two others are 1 inch below..hmm.

I think the shape may be close to a triangle? :l

igreen · Answer

No..it would have 4 sides..

igreen · Answer

Well, actually we're dealing with a cube, so..

anonymous · Answer

So the shape would have four sides?

igreen · Answer

Not exactly..a cube has more than 4 sides..so if you cut it like that I'm not exactly sure how many sides..

igreen · Answer

Any ideas? @ganeshie8

igreen · Answer

@Directrix

anonymous · Answer

@Haseeb96

anonymous · Answer

What about this one?

What 3-dimensional shape is formed when the right triangle ABC is rotated 360° about its side AB?

a cone
a square-based pyramid
a triangle-based pyramid
a cylinder

ganeshie8 · Answer

see http://gyazo.com/2342b65a1b99650bed36500c1115e459

igreen · Answer

So..?

igreen · Answer

What kind of shape would that be?

ganeshie8 · Answer

we can say this much :
the cross section has exactly 4 sides

ganeshie8 · Answer

my guess is a square, wbu ?

anonymous · Answer

I'm going to pick Rhombus. I tried square and I think the answer was incorrect.

igreen · Answer

Hmm..I'm still not that sure..the shape looks irregular to me. :l

ganeshie8 · Answer

then rhombus looks good to me!

ganeshie8 · Answer

yeah its very tricky, thats the reason i plotted the cube

anonymous · Answer

Could you possibly help me with another question?

What 3-dimensional shape is formed when the right triangle ABC is rotated 360° about its side AB?

anonymous · Answer

Why does it keep doing that lol?

ganeshie8 · Answer

go to some other question and come back

anonymous · Answer

OK it's normal for me now. WBU?

ganeshie8 · Answer

normal

ganeshie8 · Answer

do u have options ?

anonymous · Answer

a cone

a square-based pyramid

a triangle-based pyramid

a cylinder

anonymous · Answer

I chose the second one.

ganeshie8 · Answer

im guessing it would be a cone

ganeshie8 · Answer

not sure completely though as you're spinning it about hypotenuse

igreen · Answer

It wouldn't be a pyramid..because you get like infinite sides if you're rotating it 360 degrees.

igreen · Answer

And a pyramid has 4 corners.

ganeshie8 · Answer

|dw:1417527403387:dw|

ganeshie8 · Answer

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