We will see that the lateral surface area of the cone is 14 square inches.
How to find the lateral surface area?
We know that for a cone of height H and radius R, the lateral surface of the cone is:
S = 3.14*R*H
In this case, we know that eh height is 3 + 5/8 inches, and the diameter is 2 + 1/2 inches. Remember that the diameter is twice the radius, then:
R = (2 + 1/2) in = (1 + 1/4) in
Replacing that on the surface equation, we will get:
S = 3.14*( (1 + 1/4) in)*(3 + 5/8)in = 14 in^2
If you want to learn more about areas, you can read:
https://brainly.com/question/24487155