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,

$\begin{gathered} r=\frac{D}{2} \\ r=\frac{14}{2} \\ r=7\text{ in} \end{gathered}$

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,

$\begin{gathered} A_2=\frac{4\pi r^2}{2} \\ A_2=2\pi r^2 \end{gathered}$

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,

$\begin{gathered} A_{}=3\text{ }\pi r^2 \\ A=3\text{ }\pi\times7^2 \\ A=461.8in^2 \end{gathered}$

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