Question

the formula for the surface area of a sphere is 4pi^2. sphere A has aradius of 3 cm and sphere B has a radius of 6 cm. calculate the surface area of each sphere and compare their surface areas

Answer 1

It seems there's a small mistake in your provided formula for the surface area of a sphere. The correct formula for the surface area of a sphere is:

\[
\text{Surface Area} = 4\pi r^2
\]

where \( r \) is the radius of the sphere.

Now, let's calculate the surface areas for both spheres:

### Sphere A
- Radius \( r_A = 3 \) cm
\[
\text{Surface Area of Sphere A} = 4\pi (3)^2 = 4\pi (9) = 36\pi \, \text{cm}^2
\]

### Sphere B
- Radius \( r_B = 6 \) cm
\[
\text{Surface Area of Sphere B} = 4\pi (6)^2 = 4\pi (36) = 144\pi \, \text{cm}^2
\]

### Comparison of Surface Areas
- Surface Area of Sphere A: \( 36\pi \, \text{cm}^2 \)
- Surface Area of Sphere B: \( 144\pi \, \text{cm}^2 \)

To compare their surface areas, we can express the relationship:

\[
\text{Surface Area of Sphere B} = 4 \times \text{Surface Area of Sphere A}
\]

This means that the surface area of Sphere B is 4 times greater than that of Sphere A. Thus, the surface area of Sphere B is significantly larger.