Calculate and compare the surface area of sphere A, which has a radius of 4in and sphere B which has a radius of 10 in. The formula for the surface area of a sphere is 4πr2 (1 point)

Question

Sphere A has a surface area of 64π in2 and sphere B has a surface area
of 400π in2, meaning sphere B's surface area is 6.25 times as large as sphere A's.
Sphere A has a surface area of 4π in2 and sphere B has a surface area of 10π in2, meaning sphere B's surface area is 4 times as large as sphere A's.
Sphere A has a surface area of 8π in2 and sphere B has a surface area of 20π in2, meaning sphere B's surface area is 2.5 times as large as sphere A's.
Sphere A has a surface area of 16π in2 and sphere B has a surface area of 40 in2, meaning sphere B's surface area is 5 times as large as sphere A's.

Answer 1

To calculate the surface area of the spheres, we can use the formula for the surface area of a sphere:

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

For Sphere A (radius = 4 in):

\[ \text{Surface Area of Sphere A} = 4\pi (4^2) = 4\pi (16) = 64\pi , \text{in}^2 \]

For Sphere B (radius = 10 in):

\[ \text{Surface Area of Sphere B} = 4\pi (10^2) = 4\pi (100) = 400\pi , \text{in}^2 \]

Comparison:

Now, to compare the surface areas:

\[ \text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25 \]

Thus, Sphere B's surface area is \(6.25\) times larger than Sphere A's surface area.

Conclusion:

• Sphere A has a surface area of \(64\pi , \text{in}^2\)
• Sphere B has a surface area of \(400\pi , \text{in}^2\)
• Sphere B's surface area is \(6.25\) times as large as Sphere A's.

The first option you provided is correct.