Question

Find the lateral area of the cone .The lateral of the area cone is _cm2(Do not round until the final answer . Then round to the nearest whole number as needed .)

Answer 1

The formula to find the lateral area of a cone is

$LA=\frac{1}{2}rl$

Where r is the radius and l is the hypotenuse of the right triangle shown.

Let's find the hypotenuse l using the Pythagorean's Theorem

$\begin{gathered} l^2=8^2+40^2 \\ l=\sqrt[]{64+1600} \\ l=\sqrt[]{1664} \end{gathered}$

Now, we find the lateral area

$\begin{gathered} LA=\frac{1}{2}\cdot8\operatorname{cm}\cdot\sqrt[]{1664}\operatorname{cm} \\ LA\approx163(cm)^2 \end{gathered}$

Hence, the lateral surface area is 163 square centimeters.