The lateral area of a right cone which has a base diameter of four units and a height of 10 units is:
2 answers:
since it has a diameter of 4, then its radius is half that, or 2.
![\bf \textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=2\\ h=10 \end{cases}\implies LA=\pi (2)\sqrt{2^2+10^2} \\\\\\ LA=2\pi \sqrt{104}\implies LA\approx 64.076](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Blateral%20area%20of%20a%20cone%7D%5C%5C%5C%5C%20LA%3D%5Cpi%20r%5Csqrt%7Br%5E2%2Bh%5E2%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%20%5Ccline%7B1-1%7D%20r%3D2%5C%5C%20h%3D10%20%5Cend%7Bcases%7D%5Cimplies%20LA%3D%5Cpi%20%282%29%5Csqrt%7B2%5E2%2B10%5E2%7D%20%5C%5C%5C%5C%5C%5C%20LA%3D2%5Cpi%20%5Csqrt%7B104%7D%5Cimplies%20LA%5Capprox%2064.076)
Answer:![A = 64.076\ units^2](https://tex.z-dn.net/?f=A%20%3D%2064.076%5C%20units%5E2)
Step-by-step explanation:
The lateral area of right cone is calculated by the following formula
![A = \pi r *\sqrt{r^2 +h^2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cpi%20r%20%2A%5Csqrt%7Br%5E2%20%2Bh%5E2%7D)
Where r is the radius of the cone and h is the height
In this case we know that the diameter d of the base is:
![d=2r](https://tex.z-dn.net/?f=d%3D2r)
So the radius is:
![r=\frac{d}{2}\\\\r=\frac{4}{2}\\\\r=2\ units](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bd%7D%7B2%7D%5C%5C%5C%5Cr%3D%5Cfrac%7B4%7D%7B2%7D%5C%5C%5C%5Cr%3D2%5C%20units)
and
![h=10\ units](https://tex.z-dn.net/?f=h%3D10%5C%20units)
So the area is:
![A = \pi*2 *\sqrt{2^2 +10^2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cpi%2A2%20%2A%5Csqrt%7B2%5E2%20%2B10%5E2%7D)
![A = 64.076\ units^2](https://tex.z-dn.net/?f=A%20%3D%2064.076%5C%20units%5E2)
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Step-by-step explanation:
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