If a triangular cross-section with coordinates at (1, 1), (1, 4), and (3, 1) is rotated about the line x = 1, what will be the resulting three-dimensional object?

The resulting three-dimensional object will be a cone

Step-by-step explanation:  

Plot the figure to better understand the problem'

we have

a triangular cross-section with coordinates at (1, 1), (1, 4), and (3, 1)

The draw in the attached figure

we know that

When rotating a a right triangle about a leg, the three dimensional figure formed is a cone

The radius of the cone will be equal to the base of right triangle and the height of the cone will be equal to the height of the triangle

so

The radius of the cone will be equal to 2 units and the height of the cone will be 3 units

see the attached figure to better understand the problem

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

sounds & other waves originate from any vibrating object