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Answer: last option (5π√146 units²)
Step-by-step explanation:
To solve the exercise you must apply the formula for calculate the lateral area of a cone, which is shown below:
where r is the radius but L is the slant height.
As you can see in the figure attached:
But you need to find the slant height with the Pythagorean Theorem (L would be the hypotenuse):
Substitute into the formula, then:
units²