Answer :
To solve this problem, we'll break it down into two parts: (a) finding the volume of the swimming pool, and (b) finding the surface area of the scale model of the swimming pool.
(a) Volume of the swimming pool
We know that the swimming pool is a prism, and the volume of a prism is calculated using the formula:
[tex]\text{Volume} = \text{Base Area} \times \text{Height}[/tex]
In this case, the base area is given as 300 m². The depth of the swimming pool is given as 110 cm, which we need to convert into meters since the base area is in square meters. To convert centimeters to meters, divide by 100:
[tex]110 \text{ cm} = \frac{110}{100} = 1.1 \text{ m}[/tex]
Now, substitute the values into the volume formula:
[tex]\text{Volume} = 300 \text{ m}^2 \times 1.1 \text{ m} = 330 \text{ m}^3[/tex]
So, the volume of the swimming pool is 330 m³.
(b) Surface area of the model swimming pool
The scale model has a similar shape to the original swimming pool but smaller in size. The depth of the model is 5.5 cm. Since the model is a scale model, we can find the scale factor for the depth first.
[tex]\text{Scale factor for depth} = \frac{5.5 \text{ cm}}{110 \text{ cm}} = \frac{5.5}{110} = \frac{1}{20}[/tex]
Because the model is similar in all dimensions, the scale factor for the surface area is the square of the linear scale factor, so:
[tex]\text{Scale factor for surface area} = \left(\frac{1}{20}\right)^2 = \frac{1}{400}[/tex]
Given that the original swimming pool's surface area is 300 m², the surface area of the model is:
[tex]\text{Surface area of model} = 300 \text{ m}^2 \times \frac{1}{400} = 0.75 \text{ m}^2[/tex]
Thus, the surface area of the model swimming pool is 0.75 m².
