Question

The maximum load that a cylindrical column with a circular cross section can hold varies directly as the fourth power of the diameter and inversely as the square of the height. A 9 meter column 2 meters in a diameter will support 64 metric tons. How many metric tons can be supported by a column 13 meters high and 5 meters in diameter? Round to the nearest whole metric ton

Answer 1

Answer:

2396

Step-by-step explanation:

Let the diameter = d

Let the height = h

Formula

Metric Tons = k * d^4 / h^2

Solution

Metric Tons = 64

d = 2

h = 9

k = ?

(You can't do the second part by not using a ratio unless you  put k in and solve for it)

64 = 2^4 k / 9^2

64 = 8 *k / 81

64 * 81 / 8 = k

5184 / 8 = k

k = 648

Solve for the second example

Metric Tons = d^4 * k / h^2

Metric Tons = ?

d = 5

h = 13

k = 648

Metric Tons = 5^4 * 648 / 13^2

Metric Tons = 625 * 648 / 169

Metric Tons = 2396 rounded.