A closed rectangular box has a surface area of 1000 square cm. The length of the box is twice its width and the height is six times its width. What is the volume of the box?
+1005 So the surface area of a rectangular prism is 2wh + 2wl + 2hl
l = 2w
h = 6w
w = w
So replacing all terms with w, we have
2w * 6w + 2w * 2w + 2 * 2w* 6w = 12w^2 + 4w^2 + 24 w^2 = 40w^2 = 1000
w ^ 2 = 1000/40 = 25
w = sqrt(25) = 5
l = 2*5 = 10
h = 6*5 = 30
10*30*5 = the volume = 1500 cm^3
If you don't understand anything feel free to ask.
+128407 L = 2W
H = 6W
Surface area = 2 (WL + HL + HW)....so we have
1000 = 2 [ ( W (2W) + (2W)(6W) + W(6W) ] simplify
1000 = 2 [ 2W^2 + 12W^2 + 6W^2 ]
1000 = 2 [ 20W^2]
1000 = 40W^2 divide both sides by 40
1000 /40 = W^2
100/4 = W^2
25 = W^2 take the positive root
5 = W
So.....L = 2W = 10
And H = 6W = 30
So...the volume = W * L * H = ( 5) ( 10) ( 30) = 1500 cm^3
