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A community skating rink is in the shape of a rectangle with semicircles attached at the ends. The length of the rectangle is
Build a model that expresses the ice volume
How much ice is in the rink if the width is
(a)
![Check Mark](/static/check-mark.png)
The model that expresses the ice volume,
Answer to Problem 12CT
Solution:
The model that expresses the ice volume,
Explanation of Solution
Given Information:
The community skating rink is in the shape of a rectangle with semicircles attached at the ends. The length is
Explanation:
Let
The length of the rink is
So, the length of the width is
Therefore, area of rectangle
The rink is enclosed by semicircles at the ends.
These two semicircles form a circle.
As width is
Therefore, the area of circle is
Thus, total area of the rink is the sum of the area of the rectangle and the area of the circle.
Thickness of ice is 2 inches.
As other dimensions are in feet, convert 2 inches to feet.
Ice volume
Ice volume
Therefore, the model that expresses the ice volume,
(b)
![Check Mark](/static/check-mark.png)
To calculate: How muchice is in the rink if the width is
Answer to Problem 12CT
Solution:
When width is
Explanation of Solution
Given Information:
Acommunity skating rink is in the shape of a rectangle with semicircles attached at the ends. The length is
Also, width is
Formula used:
Calculation:
From part (a), model representing ice volume,
Substitute
Simplify above equation,
Therefore,
Chapter 2 Solutions
Precalculus
Additional Math Textbook Solutions
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Calculus and Its Applications (11th Edition)
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