To find the surface area of a sphere with a given radius, use the formula:
[tex]\[ A = 4 \pi r^2 \][/tex]
where:
- [tex]\( A \)[/tex] is the surface area
- [tex]\( \pi \)[/tex] is approximately 3.14159
- [tex]\( r \)[/tex] is the radius of the sphere
Given:
- Radius [tex]\( r = 10 \)[/tex] inches
Let's substitute the given radius into the formula to find the surface area.
Step 1: Square the radius
[tex]\[ r^2 = 10^2 = 100 \][/tex]
Step 2: Multiply the result by [tex]\(\pi\)[/tex]
[tex]\[ \pi \times 100 \approx 3.14159 \times 100 = 314.159 \][/tex]
Step 3: Multiply by 4
[tex]\[ 4 \times 314.159 \approx 1256.637 \][/tex]
Thus, the surface area of the sphere with a radius of 10 inches is approximately:
[tex]\[ 1256.637 \, \text{square inches} \][/tex]
So, the surface area of the sphere is [tex]\( 1256.637 \, \text{square inches} \)[/tex].
