Question

What is the lateral area of the cone?Round nearest whole, round all intermediate values to four decimals.

Answer 1

To answer this question, we can use the next formula to find the lateral area of the cone:

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

Where:

• π is approximately 3.1415926535...

,

• r = D/2. We have that the diameter is 6ft.

,

• h = height. In this case, we have h = 7ft.

We have a right circular cone, and we can use the above formula. Then, we have:

`D=6ft\Rightarrow r=(D)/(2)\Rightarrow r=(6ft)/(2)\Rightarrow r=3ft`

Then, we have:

`A_L=\pi\cdot3\cdot\sqrt[]{7^2+3^2}\Rightarrow A_L=\pi\cdot3\cdot\sqrt[]{49+9}=\pi\cdot3\cdot\sqrt[]{58}`
`√(58)=7.61577310586\approx7.6158`

Then: