Question

a 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? write your answer in terms of π and round to the nearest tenth.
volume is □ cubic centimeters.

Explanation:

Step1: Identify the shape formed

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

Step2: Determine the radius and height of the cylinder

From the grid, assume each square has side - length \(1\) centimeter. The radius \(r\) of the cylinder is \(2\) centimeters (width of the rectangle) and the height \(h\) is \(3\) centimeters (length of the rectangle).

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 \(r = 2\) and \(h=3\) into the formula:

$$V=\pi\times(2)^{2}\times3$$

$$V=\pi\times4\times3$$

$$V = 12\pi$$

Answer:

\(12\pi\)