The maximum weight that a circular column

Question

• The maximum weight that a circular column can support is directly proportional to the fourth power of its diameter and is inversely proportional to the square of its height. A 2-meter diameter column that is 8 meters in height can support 1 ton. Find the weight that a 1-meter diameter column that is 4 meters in height can support.

Answer 1

PROBLEM

 

The maximum weight that a circular column
The maximum weight that a circular column can support is directly proportional to the fourth power of its diameter and is inversely proportional to the square of its height. A 2-meter diameter column that is 8 meters in height can support 1 ton. Find the weight that a 1-meter diameter column that is 4 meters in height can support.

 

SOLUTION

 

Variation problems often require you to find the constant of variation, k, before finding the required solution.

 

Let W represent the maximum weight supported.

 

Therefore, since the maximum weight that a circular column can support is directly proportional to the fourth power of its diameter (W ∝ d⁴) and is inversely proportional to the square of its height (W ∝ 1/[h²]), W = k(d⁴/h²).

 

So, for a 2-meter diameter column that is 8 meters in height that can support 1 ton, solve for k.

 

W = k(d⁴/h²)

 

1 = k(2⁴/8²) = k(16/64) = k/4

 

k = 4

 

Now, plug k into the equation and solve for the weight that a 1-meter diameter column that is 4 meters in height can support.

 

W = 4(d⁴/h²) = 4(1⁴/4²) = 4(1/16) = 4/16 = 1/4 ton