Given:
Height of the cone, h = 7 ft
Diameter of the cone = 6 ft
Let's find the lateral surface area of the cone.
To find the lateral area of the cone, apply the formula:
[tex]A_l=\pi r\sqrt[]{h^2+r^2}[/tex]
Where r is the radius of the cone.
To find the radius, we have:
[tex]r=\frac{\text{diameter}}{2}=\frac{6}{2}=3ft[/tex]
Therefore, we have:
[tex]\begin{gathered} A_l=\pi\ast3\sqrt[]{7^2+3^2} \\ \\ A_l=3\pi\sqrt[]{49+9} \\ \\ A_l=9.4\sqrt[]{58} \\ \\ A_l=9.4248\ast7.6158 \\ \\ A_l=71.8\approx72ft^2 \end{gathered}[/tex]
Therefore, the lateral area of the cone is approximately 72 ft²
ANSWER:
[tex]\text{ 72 ft}^2[/tex]
