Answer:
The lateral area of a cone is given by the formula:
L = πrs
Where r is the radius of the base, s is the slant height, and π is pi.
We are given that the lateral area L is 587π cm^2 and the radius r is 32 cm. Substituting these values into the formula, we get:
587π = π(32)s
Simplifying, we can cancel the π on both sides of the equation:
587 = 32s
Dividing both sides by 32, we get:
s = 18.34375
Rounding to the nearest tenth, we get:
s ≈ 18.3 cm
Therefore, the slant height is approximately 18.3 cm.
Explanation: