Question

Surface area of a sphere = 4mr², where r is the radius. A sphere with a surface area of 196 cm?

Work out the radius of the sphere.

Answer 1

To find the radius of a sphere given the surface area (196 cm²), use the surface area formula A = 4πr², solve for r, and calculate r ≈ 7 cm.

Step-by-step explanation:

The student has asked how to determine the radius of a sphere given its surface area. We have the surface area formula of a sphere, which is A = 4πr², where r is the radius and A is the surface area. The student has provided a surface area of 196 cm², and we want to find r.

First, we insert the given surface area into the formula:

A = 4πr²

196 cm² = 4πr²

To solve for r, we divide both sides by 4π:

² = 196 cm² / (4π)

After dividing, we take the square root of both sides to solve for r:

r = √(196 cm² / (4π))

Performing the calculations:

r ≈ √(49.348022 cm²) ≈ 7 cm

Thus, the radius of the sphere is approximately 7 cm.