Question

#10. Find the lateral surface area of the figure discussed in problem 9.#9. Find the volume of a right solid whose height is 2 feet. Dimensions are in feet. (It comes with a picture)

Answer 1

Problem 9

The area of a trapezoid is computed using the following formula.

$\text{Area = (}\frac{a+b}{2}\text{)h}$

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

$(\frac{14+17}{2})14\text{ = 217}$

Now, the area of the half circle would be

$\text{Half circle = }\frac{\pi\cdot(7)^2}{2}\text{ = }49\pi/2$

So the area of the base would be

$217+49\pi/2\text{ }$

And since the solid is a right solid, we just multiply by the height

So, the volume of the right solid would be

$2\cdot(217+49\pi/2\text{ ) = 434 + 49}\cdot\pi$