Question

find the lateral area and surface area of the solid. round to the nearest tenth, if necessary. 5 m 14 m l ≈ m²; s ≈ m²

Explanation:

Step1: Recall lateral - area formula for cone

The lateral - area formula of a cone is $L=\pi rl$, where $r$ is the radius and $l$ is the slant height. Given $r = 5$ m and assume the height $h=14$ m. First, find the slant height $l$ using the Pythagorean theorem $l=\sqrt{h^{2}+r^{2}}=\sqrt{14^{2}+5^{2}}=\sqrt{196 + 25}=\sqrt{221}\approx14.9$ m. Then $L=\pi\times5\times14.9\approx5\times3.14\times14.9 = 234.1$ m².

Step2: Recall surface - area formula for cone

The surface - area formula of a cone is $S = L+\pi r^{2}$. We know $L\approx234.1$ m² and $\pi r^{2}=3.14\times5^{2}=3.14\times25 = 78.5$ m². So $S\approx234.1+78.5=312.6$ m².

Answer:

$L\approx234.1$ m²;
$S\approx312.6$ m²