A sphere has a surface area of 1,256 sq cm. What is its diameter?

To determine the diameter of a sphere when its surface area is known, we can use the formula for the surface area of a sphere, which is given by:

[ A = 4\pi r^2 ]

where ( A ) is the surface area, and ( r ) is the radius of the sphere.

In this case, we know the surface area is 1,256 square centimeters.

First, we can rearrange the formula to solve for the radius:

[ r^2 = \frac{A}{4\pi} ]

Substituting the known surface area into the equation:

[ r^2 = \frac{1,256}{4\pi} ]

Calculating ( 4\pi ):

[ 4\pi \approx 12.5664 ]

Now we can calculate:

[ r^2 = \frac{1,256}{12.5664} \approx 100 ]

Taking the square root of both sides gives us the radius:

[ r = \sqrt{100} = 10 \text{ cm} ]

Since the diameter ( d ) of a sphere is twice the radius, we find:

[ d = 2r =