This is based off of the paper "Scaling -- The Physics of Lilliput", but I think the following questions can be answered out of context:

1. Based on the Lilliputian reading:

A) A rectangular water tank is supported above the ground by 4 pillars 5.0 cm long whose diameters are 20 cm. If the tank were made 10x longer, wider, and deeper, how much more would the tank hold?
--> I already figured out that the answer is 1000x, which is correct.

B) In units of meters, what diameter pillars would be needed to support the weight of the new tank?
--> I am told this has to do with the pillar's cross-sectional area. If I'm not mistaken, the CSA of the pillar increases 1000x as well, but I'm not sure how you use this knowledge to determine the diameter of the new pillars.

Thanks so much in advance for any help I can get!

Yes, to get the same pressure on the tank, total area has to be 1000x.

area is proportional to diameter squared.

A=PI/4 (D^2)...

so if the diameters were 20 cm, then the new diameters should be 20sqrt(1000)

To find the answer to question A, you correctly determined that if the tank's dimensions are multiplied by 10 (in this case, length, width, and depth), the tank would hold 1000 times more water. This is because the volume of a rectangular tank is given by the formula V = l*w*h, where l is the length, w is the width, and h is the height or depth of the tank. If each of these dimensions is multiplied by 10, the new volume would be (10l)*(10w)*(10h) = 1000*l*w*h, which is 1000 times larger than the original volume.

Now let's move on to question B. The diameter of the pillars needed to support the weight of the new tank can be determined by considering the cross-sectional area of the pillars. The cross-sectional area is a measure of the surface area of a shape when it is sliced perpendicular to its length.

In this case, the pillars are cylindrical in shape. The formula for the cross-sectional area of a cylinder is A = π*r^2, where A represents the cross-sectional area and r is the radius of the cylinder. However, since the question asks for the diameter, we need to use the formula for the area of a circle, which is A = π*(d/2)^2, where d is the diameter.

You correctly mentioned that if the volume of the tank increases 1000 times, the cross-sectional area of the pillars would also increase by the same factor. This is because the weight of the water in the tank is supported by the pillars, and the increase in volume directly affects the load-bearing capacity required from the pillars.

Now, if we assume that the height of the pillars remains the same, we can use the formula for the cross-sectional area to find the diameter of the new pillars. Since the cross-sectional area increases 1000 times, we can write the equation:

A_new = 1000 * A_original

Substituting the formulas for the cross-sectional area, we get:

π*(d_new/2)^2 = 1000 * π*(d_original/2)^2

Simplifying the equation, we have:

(d_new/2)^2 = 1000 * (d_original/2)^2

Taking the square root of both sides, we get:

d_new/2 = √(1000 * d_original/2)

d_new/2 = (√1000/√2) * d_original/2

Simplifying further, we have:

d_new = (√1000/√2) * d_original

d_new = (√1000/√2) * (20 cm)

Evaluating this expression, we find that:

d_new ≈ 44.7 cm

Therefore, the diameter of the new pillars would need to be approximately 44.7 cm (or the nearest practical value in meters) to support the weight of the larger tank.