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

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

• A. 20 cm
• B. 10 cm
• C. 314 cm
• D. 157 cm

Answer: (A)

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 =

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 =