Final answer:
The height of a cone is four-thirds times the radius. The slant height can be found using the formula πr × s = 135, where 'r' is the radius. The slant height is 202.5 / π × r units.
Step-by-step explanation:
The height of a cone is four-thirds times the radius. The lateral area is 135 square units. To find the slant height of the cone, we need to first find the radius. Let's call the radius 'r'. According to the given information, the height of the cone is (4/3)r. The lateral area of a cone can be found using the formula πr × s, where 's' is the slant height. So, we have the equation πr × s = 135. Now, we can solve for 's'.
First, let's rearrange the equation to isolate 's': s = 135 / πr. Now substitute the expression for height into the equation: s = 135 / π(4/3)r = 135 / (4π/3) × r = 405 / (4π) × r = 202.5 / π × r. Therefore, the slant height of the cone is 202.5 / π × r units.