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Question

A cheesemaker makes portions of cheese by cutting a cylindrical wheel of cheese into wedges. If the given wedge is 6 inches thick and its dimension is as given, then find its volume.


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Solution

Picturing the wedge as a part of the wheel of cheese, we find:


Radius of the wheel=10 inCircumference of the wheel =2π×(radius) =2π×10 in =20π in

We know,
Arc length = Circumference×θ°360°
θ°=Arc length of a circleCircumference×360°

Length of the arc of the cheese wedge=10π3 in

Angle of the wedge=Length of the arcCircumference of the wheel×360°=(10π3÷20π)×360°=(10π3×120π)×360°=16×360°=60°

Now, the volume of the wedge can be calculated as:

Volume of the wedge =Angle of wedgeTotal angle×Volume of wheel

We know that the wheel of cheese is a cylinder with a height of 6 inches.

Volume of the wheel =π(radius)2×h =π×102×6 =π×100×6 =600π cu in

Volume of the wedge =60°360°×600 =6006 =100 cu in

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