Final answer:
The slant height of the cone, given a lateral area of 6 pi square inches and a radius of 1.2 inches, is calculated using the lateral surface area formula and has a value of 5 inches.
Step-by-step explanation:
To find the slant height of a cone given the lateral area and the radius, we use the formula for the lateral surface area of a cone, which is L = π r l, where L is the lateral area, r is the radius, and l is the slant height. In this case, we are given that the lateral area L is 6 π square inches and the radius r is 1.2 inches. Plugging these values into the formula and solving for l gives us:
L = π r l
6 π = π × 1.2 × l
l = × 6 π / (π × 1.2)
Calculating the value for the slant height l:
l = 6 / 1.2
l = 5 inches
Therefore, the slant height of the cone is 5 inches.