Question

What is the lateral area of the cone ?The lateral area of the cone is _ ft2.(Round the final answer to the nearest whole number as needed . Round all intermediate values to four decimal places as needed .)

Answer 1

We have the following equation to find the lateral area of the cone:

$L=\pi\cdot r\cdot\sqrt[]{r^2+h^2}$

where 'r' is the radius of the base and 'h' is the height.

In this case, we have the following:

$\begin{gathered} r=\frac{d}{2}=\frac{6}{2}=3 \\ h=8 \end{gathered}$

then, using the equation above, we get:

$\begin{gathered} L=(3.14)(3)\cdot\sqrt[]{(3^2+(8)^2}=9.42\cdot\sqrt[]{9+64}=9.42\cdot\sqrt[]{73}=80.48 \\ \Rightarrow L=80.48ft^2\approx81ft^2^{} \end{gathered}$

therefore, the lateral area of the cone is 80.48 ft^2