Question

brown, zacariah
21 - 2a math 3 semester 1 high school mid - term
each grid square has sides of length 1 centimeter. what is the exact volume of the solid formed by rotating this two - dimensional figure around the bolded horizontal axis? express in terms of π or round to the nearest tenth.
the volume is □ cubic centimeters.

Explanation:

Step1: Determine the shape of the solid

When a rectangle is rotated around one of its sides (the bolded horizontal axis in this case), the solid formed is a cylinder.

Step2: Identify the radius and height of the cylinder

From the grid, the width of the rectangle (which becomes the radius \(r\) of the cylinder) is \(3\) centimeters (since each square has side - length \(1\) cm). The height \(h\) of the rectangle (which becomes the height of the cylinder) is \(4\) centimeters.

Step3: 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 \(h=4\) into the formula:

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Answer:

\(36\pi\)