Question

Find the following measure for this figure.

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

Answer 1

The correct answer is 5√146π square units

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)

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=√(11^2+5^2)=√(146)`

Substitute into the formula, then:

`LA=(5)(√(146))\pi=5\pi\ \sqrt{146`units²