A rectangular water tank is supported above the ground by four pillars 5.0 m long whose diameters are 20 cm. If the tank were made 10 times longer, wider, and deeper, what diameter pillars would be needed? How much more water would the tank hold?
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Not enough data given. The only result we can state is the 10 fold increase in each of the dimensions is that the volume would be 1000 time greater
To determine the diameter of the pillars needed for the larger tank, we can use the concept of similar triangles. The ratio of corresponding sides in similar triangles is equal.
Let's assume the original tank has length L, width W, and height H. The corresponding dimensions of the larger tank would be 10L, 10W, and 10H.
To find the diameter of the new pillars, we need to consider the ratio of the lengths. Since the ratio of the new tank's length to the original tank's length is 10:1, the ratio of the new pillars' diameter to the original pillars' diameter would also be 10:1.
Given that the diameter of the original pillars is 20 cm, the diameter of the new pillars would be 10 times larger, which is:
New diameter = 10 * 20 cm = 200 cm = 2 m
Therefore, the new pillars would need to have a diameter of 2 meters.
Now, let's calculate the difference in water holding capacity between the original and larger tank. Since water capacity is determined by the volume, we need to consider the ratio of volumes.
The volume of the original tank is given by V₁ = L * W * H, and the volume of the larger tank would be V₂ = (10L) * (10W) * (10H) = 1000 * V₁.
The difference in water holding capacity between the two tanks would be:
Delta V = V₂ - V₁ = 1000 * V₁ - V₁ = 999 * V₁
Therefore, the larger tank would hold 999 times more water than the original tank.