calculate and compare the surface area of sphere A, which has a radius of 6 in., and sphere B, which has a radius of 24 in. the formula for the surface area of a sphere is 4piR^2

1 answer

To calculate the surface area of each sphere, we will use the formula for the surface area of a sphere:

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

Sphere A

  • Radius \( R_A = 6 \) inches

\[ \text{Surface Area of Sphere A} = 4\pi (6)^2 = 4\pi \times 36 = 144\pi \ \text{square inches} \]

Sphere B

  • Radius \( R_B = 24 \) inches

\[ \text{Surface Area of Sphere B} = 4\pi (24)^2 = 4\pi \times 576 = 2304\pi \ \text{square inches} \]

Comparison

Now, we can compare the surface areas of both spheres:

  • Surface Area of Sphere A: \( 144\pi \) square inches
  • Surface Area of Sphere B: \( 2304\pi \) square inches

To see how much larger Sphere B is compared to Sphere A, we can calculate the ratio of their surface areas:

\[ \text{Ratio} = \frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \]

Conclusion

Sphere B has a surface area that is 16 times larger than that of Sphere A.

  • Surface Area of Sphere A: \( 144\pi \) square inches
  • Surface Area of Sphere B: \( 2304\pi \) square inches
  • Sphere B's surface area is 16 times that of Sphere A.