Question

Find the following measure for this figure.

Answer 1

Answer:

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

Answer 2

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:

 $LA=r*L*\pi$

where r is the radius but L is the slant height.

As you can see in the figure attached:

$r=5$

But you need to find the slant height with the Pythagorean Theorem (L would be the hypotenuse):

$L=\sqrt{11^2+5^2}=\sqrt{146}$

Substitute into the formula, then:

 $LA=(5)(\sqrt{146})\pi=5\pi\ \sqrt{146$units²