The surface area of a sphere is found by the formula [tex]A = 4 \pi r^2[/tex]. Find the surface area for the following radius.

Radius: [tex]10[/tex] inches



Answer :

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].