Geometry: Volume and Surface Area

[vampirewitchreine]

Sorry if the figure is so difficult to read the numbers on. In order it's 5, 3*the square root of 2, 2, 3 and 3

net
solid (how I assume that it should look once it's all connected)

Sketch the figure that each net fold into (see above images). Then find it's volume and surface area.

I do understand how to do both volume and surface area, but I can't seem to figure it out with this once. Maybe it's the way the numbers are set up that's throwing me off or something. If someone could help walk me through how to do this, I would greatly appreciate it.

 

[Unknown008]

Can you find the surface area for this one? You just need to add the individual areas of each side in the exploded view (or net as you called it).

As for the volume, the simplest way is to understand that it's a prism with a trapezoid cross section. Which means, multiply the depth by the area of one of the trapezium

Can you try this out?

 

[vampirewitchreine]

Can you find the surface area for this one? You just need to add the individual areas of each side in the exploded view (or net as you called it).

As for the volume, the simplest way is to understand that it's a prism with a trapezoid cross section. Which means, multiply the depth by the area of one of the trapezium

Can you try this out?

Okay, so the surface area would come out at follows?:

I have each base (the trapezoids) as:
½ (5+2)(3)
½(7)(3)
3.5*3= 10.5

then the first rectangle as:
5*3= 15

the one directly above it as:
3*sqrt(2)*3= about 12.73

then the little rectangle as:
2*3= 6

and then the square as:
3*3= 9

Then all of them together:
(2*10.5)+15+12.73+6+9= 63.3


As for the volume, could you explain what the depth would be (probably a stupid question, but I'm asking anyway).

 

[Unknown008]

I think you mean 63.73 square units

Otherwise, yes, that's good.

And in the next part, 3 will be the depth. The depth is perpendicular to the cross section, which is the shape you get if you go on taking slices off the shape in all.

For example, take a cylinder. Here, the cross section is a circle, because if you cut a slice of circle off the cylinder, you sill still get another circle of the exact same size. The same thing here; the cross section will be the trapezium and hence, the depth is the length of side 3.

 

[vampirewitchreine]

>.< That was what I meant. I was changing it because I forgot to add 10.5 twice and didn't pay attention when I posted it. (And would have had the incorrect answer of 53.23)

Okay, so that would mean that the volume works out like this?:
V= [½(5+2)(3)](3)
V=[½(7)(3)](3)
V=(3.5*3)(3)
V=10.5(3)
V=31.5

 

[Unknown008]

Yes, that's it

 

[Unknown008]

Okay, I'm tired from the load of work I had today, so I'll try to calculate it.

Area of trapezium = $\displaystyle \dfrac12 (l_1 + l_2)(h) = \dfrac12 (5+2)(3) = 10.5\ units^2$

Volume = $\displaystyle 10.5\times 3 = 31.5\ units^3$

 

[Unknown008]

Nah, I don't think so. Those brains I tell you, it's like they know when to get brain-farts

 

[vampirewitchreine]

And to you Hazel: you seem quite smart for a witch

Just curious, why do you call me Hazel? Is there someone else around with a similar user name or something?