calculate and compare the surface area of sphere A, which has a radius of 2 in., and sphere B, which has a radius of 10in. The formula for the surface area of a sphere is 4piR^2

1 answer

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

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

Sphere A (Radius = 2 in)

  1. Calculate \( R^2 \): \[ R^2 = 2^2 = 4 \]
  2. Plug it into the surface area formula: \[ \text{Surface Area}_A = 4\pi \times 4 = 16\pi \text{ square inches} \]

Sphere B (Radius = 10 in)

  1. Calculate \( R^2 \): \[ R^2 = 10^2 = 100 \]
  2. Plug it into the surface area formula: \[ \text{Surface Area}_B = 4\pi \times 100 = 400\pi \text{ square inches} \]

Comparison

Now let's compare the surface areas of the two spheres:

  • Sphere A: \( 16\pi \) square inches
  • Sphere B: \( 400\pi \) square inches

To express how they relate to each other, we can calculate the ratio of their surface areas:

\[ \frac{\text{Surface Area}_A}{\text{Surface Area}_B} = \frac{16\pi}{400\pi} = \frac{16}{400} = \frac{1}{25} \]

So, Sphere B has 25 times the surface area of Sphere A.

Final Results

  • Surface Area of Sphere A: \( 16\pi \) square inches
  • Surface Area of Sphere B: \( 400\pi \) square inches
  • Sphere B is 25 times larger in surface area than Sphere A.