Find the following measure for this figure.

lateral area =
55 square units
5√(47) square units
5√(146) square units

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

The correct answer is 5√146π  square units

Step-by-step explanation:

From the figure we can see a cone

Points to remember

Lateral surface area of cone = πrl

r - Radius of cone

l - Slant height of cone

To find the slant height

From figure we get,

r = 5 units and height = 11 units

Slant height² = radius² + height² =  5² + 11² = 25 + 121 = 146

Slant height = √146 units

To find the lateral area

lateral area = πrl =  π * 5 * √146  = 5√146π  square units

The correct answer is 5√146π  square units

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