Question

I need to find the surface area. it's a cut sphere with a diameter of 14.

Answer 1

Given data:

The diameter of the cut sphere, D=14 in.

The radius of the cut sphere is,

`\begin{gathered} r=(D)/(2) \\ r=(14)/(2) \\ r=7\text{ in} \end{gathered}`

The cut sphere is called a hemisphere.

The surface area of a sphere is

`A_1=4\pi r^2`

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

`\begin{gathered} A_2=(4\pi r^2)/(2) \\ A_2=2\pi r^2 \end{gathered}`

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

`A_3=\pi r^2`

Therefore, the total area of the hemisphere is,

`\begin{gathered} A=A_2+A_3 \\ A=2\text{ }\pi r^2+\pi r^2 \\ A=3\text{ }\pi r^2 \end{gathered}`

The total surface area of a hemisphere is,

`\begin{gathered} A_{}=3\text{ }\pi r^2 \\ A=3\text{ }\pi*7^2 \\ A=461.8in^2 \end{gathered}`

Therefore, the total surface area of the cut sphere is 461.8 square inches.