Question

find the following measure for this figure.
lateral area =
6√(142) π square units
6√(146) π square units
66 π square units

Explanation:

Step1: Recall lateral area formula

Lateral area of cone: $LA = \pi r l$ (r=radius, l=slant height)

Step2: Find slant height l

Use Pythagoras: $l = \sqrt{r^2 + h^2} = \sqrt{6^2 + 11^2} = \sqrt{36 + 121} = \sqrt{157}$

Step3: Calculate lateral area

$LA = \pi \times 6 \times \sqrt{157} = 6\sqrt{157}\pi$

Answer:

B. $6\sqrt{157}\pi$ square units