Answer: last option (5π√146 units²)
Step-by-step explanation:
To solve the exercise you must apply the formula for calculate the lateral area of a cone, which is shown below:

where r is the radius but L is the slant height.
As you can see in the figure attached:

But you need to find the slant height with the Pythagorean Theorem (L would be the hypotenuse):

Substitute into the formula, then:
units²
Answer:
y - 4 = (4/3)(x - 1)
Step-by-step explanation:
point slope form is
y - y1 = m(x - x1)
m is the slope
(x1, y1) is a point on the line
----------------------------
for m = 4/3 and (x1, y1) = (1, 4)
y - 4 = (4/3)(x - 1)