Germane is making a rectanglar cardboard house for his pet gerbil. He wants the house to be at least 5in. tall, 6in. wide, and 8in. long. What is the minimum surface area, if the base of the rectangular prism is open? Please show work to help me understand.
2007-04-12 15:24:42 · 8 answers · asked by Bryan 3 in Science & Mathematics ➔ Mathematics
length = 8 = l
breadth= 6 = b
height = 5 = h
l *b = 48 {ceiling}
b * h = 30 {front and back face of house }
l * h = 40 {two sides}
48+(2*30)+(2*40)
=188(ans)
2007-04-12 15:33:20 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Here you go, step by step.
Your rectangular prism has only 5 sides because the bottom is open. You have the front and back which will be identical. You have the two side pieces which will also be identical and then you have the one top piece.
Front and Back (80 sq. in.)
The front of the house is 8 inches long and stands up 5 inches. So, the front is 5 by 8. Area is LxW which is 8x5=40. You have the back which is the same, so that is another 40.
Front and back is 80 sq. in.
Two Side (60 sq. in)
The sides are 6 inches deep and 5 inches high, that 6 by 5.
A= LxW = 6x5 = 30, and there are two identical sides so that is 60 sq. in.
The Top (48 sq. in.)
Has the same length as the front and the same width as the side so it has to be 8 by 6. A = LxW, so A = 8x6 = 48
The total surface area is
80 + 60 + 48 = 188 sq. in.
2007-04-12 22:43:41 · answer #2 · answered by Critters 7 · 1⤊ 0⤋
calculate the area of the top, and the four walls, then add.
walls:
5 x 6
5 x 6
5 x 8
5 x 8
top:
6x8
(2(5 x 6)) + (2(5 x 8)) + (6 x 8) =
(60) + (80) + (48) =
188 inches square
the base of the rectangular prism is the floor, so you don't include it. If you did, you could just add (6 x 8) again, to get the entire surface area including the floor.
Hope that helps.
-Rob
2007-04-12 22:33:18 · answer #3 · answered by Rob S 3 · 1⤊ 0⤋
There are five surfaces: the two front sides each have area (8*5)=40; the two sides each have area (6*5)=30; finally, the top has area 8*6=48. Now just add them all up to get 188.
2007-04-12 22:29:12 · answer #4 · answered by bruinfan 7 · 0⤊ 0⤋
2 pieces
5 inches tall x 6 inches wide =30 inches each x2 = 60 inches sq.
2 pieces
5 inches tall x 8 inches long = 40 inches each x 2 = 80 inches sq.
60 + 80 = 140 in sq. needed for house
2007-04-12 22:28:24 · answer #5 · answered by mnnydb 3 · 0⤊ 0⤋
the house has 5 sides.
the area of the of the front=widthx height
=6x5=30
This area is the same as the back of teh house so u jsut multiply by two so you get
30x2=60
Then the areao the other sides of the house =lengthxheight
=8x5= 40
You multiply by 2 and get 80
Then the top of the house is = lengthx width
=8x6=48
Add em up and get 188
I know its been answered but maybe this makes it easier to understand.
2007-04-12 22:39:42 · answer #6 · answered by marcus83 1 · 1⤊ 0⤋
Just draw out the house and label all the sides how long they are. Then find the area for each side and add them up.
2007-04-12 22:32:50 · answer #7 · answered by yankee112792 2 · 0⤊ 0⤋
Word problem? By crikey, this is math and physics! *goes back to her dictionaries*
2007-04-12 22:28:16 · answer #8 · answered by Lineya 4 · 0⤊ 0⤋