Answer:
l ≈ 17.72 cm
Explanation:
Let's denote the slant height of the cone as "l" and the radius of the cone as "r".
We know that the total surface area of the cone is given by:
πrl + πr^2
And we also know that the curved surface area of the cone is given by:
πrl
So we can write two equations using these formulas:
πrl + πr^2 = 704 (1)
πrl = 550 (2)
Now, we can solve for "l" by substituting equation (2) into equation (1):
550 + πr^2 = 704
πr^2 = 154
r^2 = 154/π
r ≈ 6.223 cm
Substituting this value of "r" into equation (2), we get:
πl(6.223) = 550
l ≈ 17.72 cm
Therefore, the slant height of the cone is approximately 17.72 cm.