The record height of a man to date is 8 feet 11 inches (107 inches). If all men had identical body types, their weights would vary directly as the cube of their heights. Assume that all men do have identical body types. If a man who is 5 feet 10 inches tall (70 inches) weighs 175 pounds, approximately how much would a man with a height of 9 feet left parenthesis 108 inches right parenthesis weigh?
175 * (108/70)^3 = ?
To solve this problem, we need to set up a proportion based on the given information. Remember that the weights of men vary directly as the cube of their heights.
Let's represent the weight of a man with a height of 5 feet 10 inches (70 inches) as W1, and the weight of a man with a height of 9 feet (108 inches) as W2.
According to the problem, we have:
W1 = 175 pounds (weight of a man with a height of 70 inches)
Now, we can write the proportion:
W1/W2 = (H1^3)/(H2^3)
Plugging in the given values, we get:
175/W2 = (70^3)/(108^3)
To solve for W2, we can cross multiply and solve for W2:
W2 = (175 * 108^3)/(70^3)
Calculating this, we find:
W2 ≈ 446.11 pounds
Therefore, a man with a height of 9 feet (108 inches) would weigh approximately 446.11 pounds.
To solve this problem, we can set up a proportion using the given information.
First, let's convert the height of the first man from 5 feet 10 inches to 70 inches.
Next, we can set up the proportion using the given information about the weights varying directly as the cube of the heights:
(Weight of man 1) / (Height of man 1)^3 = (Weight of man 2) / (Height of man 2)^3
Plugging in the values, we get:
175 / 70^3 = (Weight of man 2) / 108^3
Now, we can solve for the weight of man 2 by cross-multiplying and then dividing:
(Weight of man 2) = (175 / 70^3) * 108^3
Calculating this expression, we find that the weight of a man with a height of 9 feet (108 inches) would be approximately 364.29 pounds.
We'll use W to represent weight, k to represent the constant and H to represent hight.
W=kH^3 (weight =constant x H cubed)
to find our constant we will use W175 and H70 from the question above
175=k70^3
now to separate k from 70 cubed we divide both side of the equation by 70^3. This gives us our k value.
175/70^=k
k=.000510204
then we use the constant we found to solve for the weight of the man whos hight is 108"
W=.000510204x108^3
W=.000510204x1259712
W=643lb