Question

question 16
each small square represents 1 square centimeter.
what is the volume of the solid formed by rotating this two - dimensional figure around the vertical axis shown?
leave answer in terms of \pi\.

Explanation:

Step1: Determine the radius and height of the cylinder

• Each small square represents \(1\) square centimeter, so the side - length of each small square is \(1\) centimeter.
• The radius \(r\) of the base of the cylinder formed by rotation: The horizontal distance from the axis of rotation to the right - most side of the blue square is \(3\) centimeters, so \(r = 3\) cm.
• The height \(h\) of the cylinder: The vertical length of the blue square is \(3\) centimeters, so \(h=3\) cm.

Step2: Use the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\).
Substitute \(r = 3\) and \(h = 3\) into the formula:

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Answer:

\(27\pi\) cubic centimeters