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Using the vertices of a 9-in. square as centers, and radii equal to 3 in., four quadrants are described within the square. If the figure thus formed is the uniform cross section of a cylinder of element 7 in., find the volume and total area of the cylinder.
Solution:
To illustrate the problem, it is better to draw the figure which is the cross section as follows
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| Photo by Math Principles in Everyday Life |
As you can see from the figure above that there are four quarter circles which is equal to one circle. Hence, the area of the shaded region which is also the base of a right cylinder is
Therefore, the volume of a right cylinder is
Next, we need to get the perimeter of the base of the shaded region which is equal to the sum of the circumference of a whole circle and the length of the four line segments between the arcs of the quarter circles as follows
Hence, the surface or lateral area of a right cylinder is
Therefore, the total area of a circular cylinder is
