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

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:

`A_l=\pi r\sqrt[]{h^2+r^2}`

Where r is the radius of the cone.

To find the radius, we have:

`r=\frac{\text{diameter}}{2}=(6)/(2)=3ft`

Therefore, we have:

`\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}`

Therefore, the lateral area of the cone is approximately 72 ft²

ANSWER:

`\text{ 72 ft}^2`