Geometric Modeling Math Example 4

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Example 4

hard

A swimming pool has a rectangular flat bottom (

20\,\text{m}\times 8\,\text{m}

) with a semicircular end on each short side (the pool shape is a rectangle with two semicircles). Find the total surface area of the pool floor (water-contact area, flat only).

Solution

1
Step 1: The floor consists of a rectangle and two semicircles. The two semicircles of radius $4$ m form one complete circle.
2
Step 2: Rectangle area $= 20 \times 8 = 160$ m $^2$ .
3
Step 3: Circle area $= \pi r^2 = \pi(4)^2 = 16\pi \approx 50.3$ m $^2$ .
4
Step 4: Total area $= 160 + 16\pi \approx 210.3$ m $^2$ .

Answer

Total floor area

= 160 + 16\pi \approx 210.3

^2

Complex shapes are modelled by decomposing them into simpler geometric pieces. Here the pool floor is a rectangle plus a full circle (two semicircles). Adding the areas of component shapes gives the total — a fundamental technique in geometric modelling.

About Geometric Modeling

Using geometric shapes and their relationships to represent, approximate, and analyze real-world objects and situations.

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Example 2 medium

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Example 3 easy

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