You have two boxes of the same shape that hold flour. The larger box holds twice as much flour as the smaller one. You conclude that it would take you _?_ times as much paint to paint the larger box than it would take you to paint the smaller box.
2006-10-22 14:15:42 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
V2 = 2V1
As similar shapes
L2=k*L1 where k = 2^⅓
and S2 = h*S1 where h = k² = 2^⅔
So S2 = 2^⅔*S1
≈ 1.5874*S1
which means that the big box would require is 58.74% more paint
2006-10-22 14:25:35 · answer #1 · answered by Wal C 6 · 0⤊ 0⤋
2
2006-10-23 12:10:46 · answer #2 · answered by arpalu69 1 · 0⤊ 0⤋
Assume that they're cubical boxes. the small box has sides of length l and holds v amount so v = l^3. The large box holds 2v so it's sides must be cube root(2) longer. The small box has 6 sides of l² area so it has 6l² units of surface area. The large box has 6(cube root(2)*l)² units of surface area to cover, so it will take 2^(2/3) times as much paint as the small box. (2^(2/3) = 1.587)
Doug
2006-10-22 21:24:54 · answer #3 · answered by doug_donaghue 7 · 0⤊ 0⤋
X ,Y and Z -> first box’s dimensions
its area A1= 2(XY + XZ +YZ)
its volume V1 = XYZ
aX,aY AND aZ -> Second box's dimensions
its area A2 =2 a^2(XY + XZ +YZ) = a^2 A1
its volume V2 = a^3 XYZ = 2V1 = XYZ
->a^3 = 2
a=2^(1/3)
aree of box2 A2=(a^2)A1=((2^(1/3))^2) A1
A2 = 2^(2/3) A1
2006-10-22 21:31:28 · answer #4 · answered by Anas 3 · 0⤊ 0⤋
2, but this awnser is coming from a sixth grader
2006-10-22 21:53:41 · answer #5 · answered by FOBLuv 2 · 0⤊ 0⤋
the blank is 'two' pretty sure
2006-10-22 21:23:59 · answer #6 · answered by Ariel 2 · 0⤊ 0⤋
1.25992105
2006-10-22 21:23:59 · answer #7 · answered by pilly 2 · 0⤊ 0⤋