Question

each small square has sides of length 1 centimeter. what is the exact volume of the solid formed by rotating this two - dimensional figure answer in terms of π or round to the nearest tenth. the volume is cubic centimeters.

Explanation:

Step1: Determine the radius and height of the cylinder

When a rectangle is rotated about an axis (in this case, the line at the bottom of the rectangle), it forms a cylinder. The formula for the volume of a cylinder is \(V=\pi r^{2}h\). From the grid, the width of the rectangle (radius \(r\)) is \(2\) cm (since each square has side - length \(1\) cm) and the height of the rectangle (height of the cylinder \(h\)) is \(4\) cm.

Step2: Calculate the volume of the cylinder

Substitute \(r = 2\) and \(h=4\) into the formula \(V=\pi r^{2}h\).

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If we use \(\pi\approx3.14\), then \(V = 16\times3.14=50.24\approx50.2\) (rounded to the nearest tenth)

Answer:

\(16\pi\) (exact value) or \(50.2\) (rounded to the nearest tenth)