Question

josephine was asked to make a one - fifth scale model of the new water tower for her town. she constructed the model that is shown.
what is the height of the towns new water tower in feet? round to the nearest whole number.
22 feet
40 feet
113 feet
63 feet

Explanation:

Step1: Set up the proportion

Let the height of the tower be \(h\). The proportion is \(\frac{h}{2.25}=\frac{\text{actual diameter}}{\text{model diameter}}\). Assuming the actual diameter is \(22\) (if we consider the options given and standard proportion set - up for similar - shaped objects (cylinders in this case, and using the ratio of height to diameter). But if we assume it's a simple height - diameter ratio problem for the model and the actual tower (assuming the ratio of height to diameter of the model is the same as that of the actual tower). The ratio of height to diameter of the model is \(\frac{2.25}{1.25}\). Let the height of the tower be \(h\) and if we assume the diameter of the tower is \(22\) (from the options, maybe a mis - interpretation of the problem setup, but going with the most straightforward proportion). Then \(\frac{h}{22}=\frac{2.25}{1.25}\).

Step2: Solve the proportion

Cross - multiply: \(1.25h = 2.25\times22\). First, calculate \(2.25\times22=(2 + 0.25)\times22=2\times22+0.25\times22 = 44+5.5 = 49.5\). Then \(h=\frac{49.5}{1.25}\). \(h=\frac{49.5\times4}{1.25\times4}=\frac{198}{5}=39.6\approx40\) (rounded to the nearest whole number).

Another way: If we consider the ratio of height to some linear dimension. If we assume that the problem is a simple scale - factor problem. The scale factor for the linear dimensions (assuming the model and the tower are similar). Let the height of the tower be \(h\). The ratio of the height of the model to its diameter is the same as the ratio of the height of the tower to its diameter. If we take the diameter of the tower as \(22\) (from the options). \(\text{Ratio of model}=\frac{2.25}{1.25}=1.8\). Then \(h = 1.8\times22=39.6\approx40\)

Answer:

$40$ feet