Question

find the lateral area of the cone.
16 in.
6 in.
round your answer to the nearest tenth.
square inches

Explanation:

Step1: Find the slant height $l$.

Use the Pythagorean theorem $l=\sqrt{h^{2}+r^{2}}$, where $h = 16$ in and $r=6$ in. So $l=\sqrt{16^{2}+6^{2}}=\sqrt{256 + 36}=\sqrt{292}=2\sqrt{73}\approx17.1$ in.

Step2: Calculate the lateral - area formula for a cone.

The formula for the lateral area of a cone is $A=\pi rl$. Substitute $r = 6$ in and $l\approx17.1$ in. Then $A=\pi\times6\times17.1 = 102.6\pi\approx322.1$ square inches.

Answer:

$322.1$