Question

http://vtok.me/pic/2b9tB9Zj.jpg
http://vtok.me/pic/kiyhjaX3.jpg
I need help with these

Answer 1

Which would you like to start with and do you have friends that want to join?

Answer 2

Yes she came.

Answer 3

im here :D again

Answer 4

I would like to start with 1.

Answer 5

well first of all this is an pentagonic prism so it does have five sides

Answer 6

Right, so what dimensions will you need to know?

Answer 7

ummm....8,5,5,and 12:?

well the formula would be
Volume of Prism = (5/2)ash = Ah
where
a = apothem length, s = side, h = height.

Answer 8

Correct, and what dimensions do you have?

Answer 9

Would it be 6 and 6, because you could draw a line vertical in the pentagon and 8 and 10 for the rectangle when you draw a horizontal line?

Answer 10

You would divide 12 by 2 for the two triangles and add 5 and 5 since the rectangle is not separated by a horizontal line I think. Also what is an apothem length?

Answer 11

apothem is also the radius of the incircle of the polygon

Answer 12

or in this case the pentagon

Answer 13

From what I can see in the picture you are not given the apothem. However we could calculate it with \[apothem=\frac{side}{2\tan(\frac{180}{n})}\] where n is the number of sides.

Answer 14

But perhaps we are not meant to go that route. If you reflect back on the problems we did the other day, could you think of another way that we could get the volume?

Answer 15

well could we find the volme of a rectangular prism instead

Answer 16

And then?

Answer 17

subtract the unshaded parts???

Answer 18

Excellent.

Answer 19

And what would those unshaded parts be? How would you describe the shape?

Answer 20

ummm maybe triangles/triangular prisms??

Answer 21

BINGO! Yes, triangular prisms, a shape that you just found the volume of several times over.

Answer 22

So what do you get for the over all volume and for each of the triangular prisms?

Answer 23

ummm.....well one side can be 7 and then he other can be 5 and the last width can be 7

and total can be 245in cubed........i think im wrong

Answer 24

If you are doing the rectangular prism, can you draw it?

Answer 25

I think it will help you to solidify the dimensions you need to use.

Answer 26

if u dont mind......could u actually show us how to do get the answer because i am really confuzed

Answer 27

Sure. Looking at your prism you will see that they give you two maximum dimensions, the max width @ 12" and a max height @ 14". So the rectangular prism, which encompasses your pentagonal prism, had dimensions of 12x7x14