Question

yolanda is planning to put a pool in her backyard. the scaled model shown gives the reduced measures for diameter and depth.
the yard space is large enough to have a pool that has a diameter of 27 feet. if yolanda wants to keep the pool in proportion to the model, what will be the depth of the pool?
6 feet
4.5 feet
6.75 feet
5 feet

Explanation:

Step1: Set up proportion

Let \( x \) be the depth of the pool. The proportion is \(\frac{\text{model diameter}}{\text{actual diameter}}=\frac{\text{model depth}}{\text{actual depth}}\). Given model diameter \(d_{m} = 4\space cm\), actual diameter \(d_{a}=27\space ft\), model depth \(h_{m}=1\space cm\). So \(\frac{4}{27}=\frac{1}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(4x = 27\times1\).

Step3: Solve for \(x\)

Divide both sides by 4: \(x=\frac{27}{4}=6.75\).

Answer:

\(6.75\) feet