Problem 9
The area of a trapezoid is computed using the following formula.
[tex]\text{Area = (}\frac{a+b}{2}\text{)h}[/tex]
In order to use the formula, for this problem
a = 17
b = 14
h = diameter of the half circle = 2*7 = 14
Therefore using the formula for the area of a trapezoid
We have that the area of the trapezoid on the figure would be
[tex](\frac{14+17}{2})14\text{ = 217}[/tex]
Now, the area of the half circle would be
[tex]\text{Half circle = }\frac{\pi\cdot(7)^2}{2}\text{ = }49\pi/2[/tex]
So the area of the base would be
[tex]217+49\pi/2\text{ }[/tex]
And since the solid is a right solid, we just multiply by the height
So, the volume of the right solid would be
[tex]2\cdot(217+49\pi/2\text{ ) = 434 + 49}\cdot\pi[/tex]
