00:01
Okay, so i see that you need help with these two problems, and for the first one, it wants you to find the volume of the prism.
00:07
So what i would do is base times height divided by two, and then you're going to multiply it by the height of the object.
00:14
Okay? so you would do 14 times 8 divided by 2, and then you would multiply it by 12.
00:22
So 14 times 8 is 112, divided by 2 times 12.
00:31
So 112 divided by 2 is 56 times 12 is 672 inches cubed.
00:43
So you are right on this one.
00:46
A plane slices the prism as shown parallel to the bases.
00:50
Find the area of the cross section created by the slice.
00:53
So the area of the cross section is 56 inches squared.
00:59
Find the surface area of the prism to the nearest square inch.
01:03
So to find the surface area, you have three rectangles, okay, and two triangles.
01:12
So two triangles, so two times base times height divided by two plus length times width plus length times width plus length times with.
01:24
Now see, the thing is this is four and this is 14.
01:28
So i have a triangle and it's 4 and 14.
01:33
Okay, i need to find the length of the diagonal.
01:36
So i have to do, i'm going to put it over here, 4, 14.
01:41
I have to do four, use the pythagorean theorem, so 4 squared plus 14 squared equals c squared.
01:48
So 16 plus 14 squared is to 196.
01:53
And then if i add 16 and 196, i'm going to get 212.
01:59
And then finding the square root of 212, it's 14 .6.
02:09
So then what i'm going to do is, let me just erase this part.
02:17
I'm going to plug the numbers in.
02:19
So this is 14 .6.
02:22
Okay? so i have 2 times 14 times 8 divided by 2 plus there are two triangles that are 14 .6 by 12.
02:36
So 2 times 14 .6 times 12 because we have this side and the other side.
02:42
But then the bottom piece is an 8 by 12.
02:49
So i already know that 2 times multiply by 14 times 8 divided by 2 is 56 plus 2 times 14 .6 times 12 is 1717 .5.
03:09
Point two plus eight times 12 is 96 so two times 175 .2 is 350 .4 plus 96...