Final answer:
To find the lateral surface area of a cone generated by revolving a line segment about an axis, we need to determine the length of the line segment and the base radius of the cone. Then, we can use the formula A = πrℓ, where r is the radius of the base and ℓ is the slant height of the cone. Calculate ℓ using the Pythagorean theorem with the height and radius values, and then substitute the values into the formula to find the lateral surface area.
Step-by-step explanation:
To find the lateral surface area of a cone generated by revolving a line segment about an axis, we first need to determine the length of the line segment and the radius of the cone at its base. Let's use an example:
Suppose the line segment has a length of 10 units and the base radius of the cone is 5 units. We can use the formula for the lateral surface area of a cone, which is given by A = πrℓ, where r is the radius of the base and ℓ is the slant height of the cone. The slant height can be determined using the Pythagorean theorem, since it forms a right triangle with the height and the radius. In this case, the height is equal to the length of the line segment. So, we have:
Height (h) = 10 units
Radius (r) = 5 units
Slant height (ℓ) = √(r^2 + h^2) = √(5^2 + 10^2) = √125 units
Now we can calculate the lateral surface area:
A = πrℓ = 3.14 * 5 * √125 = 22.16 square units