Question

Find the radius of a sphere whose surface area is 154 cm²

Answer 1

We are given the surface area of a sphere as 154 cm². We need to find the radius of the sphere.

Step-by-Step Solution:

1. Formula for Surface Area of a Sphere:

The formula for the surface area \( A \) of a sphere is: \[ A = 4 \pi r^2 \] where \( r \) is the radius of the sphere.

2. Substitute the Given Surface Area:

We are given that the surface area \( A = 154 \, \text{cm}^2 \). Substituting this into the formula: \[ 154 = 4 \pi r^2 \]

3. Solve for the Radius \( r \):

First, divide both sides of the equation by \( 4 \pi \): \[ r^2 = \frac{154}{4 \pi} \] Using \( \pi \approx 3.14 \), we get: \[ r^2 = \frac{154}{4 \times 3.14} = \frac{154}{12.56} = 12.25 \] Now, take the square root of both sides to find \( r \): \[ r = \sqrt{12.25} = 3.5 \, \text{cm} \]

Final Answer:

The radius of the sphere is \( \boxed{3.5 \, \text{cm}} \).