Question

question
trapezoid lmno is formed when right triangle plm is cut by line on such that on || lm.
find the volume of the solid generated when the trapezoid is rotated about side ol. round
your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify the formula for the volume of a frustum of a cone

The volume \( V \) of a frustum of a cone is given by \( V=\frac{1}{3}\pi h(r_1^{2}+r_1r_2 + r_2^{2})\), where \( h\) is the height of the frustum, \( r_1\) is the radius of the larger base, and \( r_2\) is the radius of the smaller base. When the trapezoid \( LMNO\) is rotated about \( OL\), the height \( h = 6\), \( r_1=14\), and \( r_2 = 7\).

Step2: Substitute the values into the formula

Substitute \( h = 6\), \( r_1=14\), and \( r_2 = 7\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Calculate the numerical value

Using \( \pi\approx3.14\), we have \( V = 686\times3.14=2154.04\)

Answer:

\(2154.0\)