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.

Answer 1

To calculate the surface area of spheres A and B, we will use the formula for the surface area of a sphere, which is:

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

Sphere A:

1. Radius (R) = 6 inches
2. Surface Area Calculation: \[ \text{Surface Area of Sphere A} = 4\pi (6)^2 = 4\pi (36) = 144\pi \text{ square inches} \]

Sphere B:

1. Radius (R) = 24 inches
2. Surface Area Calculation: \[ \text{Surface Area of Sphere B} = 4\pi (24)^2 = 4\pi (576) = 2304\pi \text{ square inches} \]

Comparison:

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

To compare the surface areas numerically, we can calculate the approximate values using \( \pi \approx 3.14 \):

• Surface Area of Sphere A: \[ 144\pi \approx 144 \times 3.14 \approx 452.16 \text{ square inches} \]
• Surface Area of Sphere B: \[ 2304\pi \approx 2304 \times 3.14 \approx 7238.56 \text{ square inches} \]

Summary:

• Sphere A: \( 144\pi \) square inches (approx. 452.16 square inches)
• Sphere B: \( 2304\pi \) square inches (approx. 7238.56 square inches)

Sphere B has a surface area that is significantly larger than that of Sphere A. In fact, by comparing the surface areas in terms of \( \pi \):

• The ratio of the surface area of Sphere B to Sphere A is: \[ \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16 \] This means Sphere B's surface area is 16 times greater than that of Sphere A.