jem3 said:
If a man who is 5 feet 10 inches tall weighs 170 pounds how much does a man of the same body type who is 8 feet 2 inches tall weigh?
I'm not sure what to do with this variation problem. I converted the heights into inches and plugged the
weight and heights given into the formula y=kx^3, but I can't seam to get a reasonable answer. Perhaps I'm
using the wrong formula or I'm just plugging the information in wrong. Anyway, I can't seam to get it right.
Here's what I've tried: 5'10"=70inches and 8'2"=98inches
y=170 k(70^3)
170=34000
K=170/34000k
y=(170/34000k)(98^3)
y=4705.96?
If two figures are SIMILAR (and "same body type" would indicate that), then the ratio of the volumes of the figures is the CUBE of the ratio of a pair of corresponding lengths.
Suppose figures 1 and 2 are similar, that h[sub:1teoyjoo]1[/sub:1teoyjoo] represents the height of figure 1, and that h[sub:1teoyjoo]2[/sub:1teoyjoo] represents the height of figure 2.
Then, the ratio of corresponding lengths is h[sub:1teoyjoo]1[/sub:1teoyjoo] / h[sub:1teoyjoo]2[/sub:1teoyjoo].
Let V[sub:1teoyjoo]1[/sub:1teoyjoo] = volume (or weight, in this problem) of figure 1, and let V[sub:1teoyjoo]2[/sub:1teoyjoo] = volume (or weight) of figure 2.
Since the ratio of the volumes of two similar figures is the CUBE of the ratio of a pair of corresponding lengths,
V[sub:1teoyjoo]1[/sub:1teoyjoo] / V[sub:1teoyjoo]2[/sub:1teoyjoo] = (h[sub:1teoyjoo]1[/sub:1teoyjoo] / h[sub:1teoyjoo]2[/sub:1teoyjoo])[sup:1teoyjoo]3[/sup:1teoyjoo]
Now, you know the first man is 5 feet 10 inches tall...let's convert that to inches: 5*12 inches + 10 inches = 70 inches
The questioned person is 8 feet 2 inches tall...convert that to inches, also: 8*12 inches + 2 inches = 98 inches
Then h[sub:1teoyjoo]1[/sub:1teoyjoo] = 70 inches and h[sub:1teoyjoo]2[/sub:1teoyjoo] = 98 inches.
The weight (volume) of the man is 170 lbs...that's V[sub:1teoyjoo]1[/sub:1teoyjoo]
We don't know the weight of the "really tall" man...call that "x"
Substitute into the formula.
V[sub:1teoyjoo]1[/sub:1teoyjoo] / V[sub:1teoyjoo]2[/sub:1teoyjoo] = (h[sub:1teoyjoo]1[/sub:1teoyjoo] / h[sub:1teoyjoo]2[/sub:1teoyjoo])[sup:1teoyjoo]3[/sup:1teoyjoo]
150 / x = (70/98)[sup:1teoyjoo]3[/sup:1teoyjoo]
Now, solving for x is up to you.
