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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. T...Question
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 4π2. (1 point)
Sphere A has a surface area of 144π in.2 and sphere B has a surface area of O 2, 304π in.2. This means that sphere B's surface area is 16 times as large as sphere A's.
Sphere A has a surface area of 36π in.2 and sphere B has a surface area of 576π in.2. This means that sphere B's surface area is 16 times as large as sphere A's.
Sphere A has a surface area of 6π in.2 and sphere B has a surface area of 24π in.2. This means that sphere B's surface area is 4 times as large as sphere A's.
Sphere A has a surface area of 24π in.2 and sphere B has a surface area of 96 in.2. This means that sphere B's surface area is 4 times as large as sphere A's.
Sphere A has a surface area of 144π in.2 and sphere B has a surface area of O 2, 304π in.2. This means that sphere B's surface area is 16 times as large as sphere A's.
Sphere A has a surface area of 36π in.2 and sphere B has a surface area of 576π in.2. This means that sphere B's surface area is 16 times as large as sphere A's.
Sphere A has a surface area of 6π in.2 and sphere B has a surface area of 24π in.2. This means that sphere B's surface area is 4 times as large as sphere A's.
Sphere A has a surface area of 24π in.2 and sphere B has a surface area of 96 in.2. This means that sphere B's surface area is 4 times as large as sphere A's.
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GPT-4o mini
To find the surface area of each sphere, we will use the formula for the surface area of a sphere, \( S = 4\pi r^2 \), where \( r \) is the radius of the sphere.
**Calculating Sphere A:**
- Radius of sphere A, \( r_A = 6 \) inches
- Surface area of sphere A:
\[
S_A = 4\pi (6^2) = 4\pi (36) = 144\pi \, \text{in}^2
\]
**Calculating Sphere B:**
- Radius of sphere B, \( r_B = 24 \) inches
- Surface area of sphere B:
\[
S_B = 4\pi (24^2) = 4\pi (576) = 2304\pi \, \text{in}^2
\]
Now we have:
- Surface area of sphere A is \( 144\pi \, \text{in}^2 \)
- Surface area of sphere B is \( 2304\pi \, \text{in}^2 \)
Next, we can compare the surface areas of the two spheres:
- To find how many times larger the surface area of sphere B is in comparison to sphere A, we divide the surface area of sphere B by the surface area of sphere A:
\[
\text{Ratio} = \frac{S_B}{S_A} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16
\]
Thus, sphere B's surface area is 16 times as large as sphere A's.
Therefore, the correct comparison is:
**Sphere A has a surface area of \( 144\pi \, \text{in}^2 \) and sphere B has a surface area of \( 2304\pi \, \text{in}^2 \). This means that sphere B's surface area is 16 times as large as sphere A's.**
**Calculating Sphere A:**
- Radius of sphere A, \( r_A = 6 \) inches
- Surface area of sphere A:
\[
S_A = 4\pi (6^2) = 4\pi (36) = 144\pi \, \text{in}^2
\]
**Calculating Sphere B:**
- Radius of sphere B, \( r_B = 24 \) inches
- Surface area of sphere B:
\[
S_B = 4\pi (24^2) = 4\pi (576) = 2304\pi \, \text{in}^2
\]
Now we have:
- Surface area of sphere A is \( 144\pi \, \text{in}^2 \)
- Surface area of sphere B is \( 2304\pi \, \text{in}^2 \)
Next, we can compare the surface areas of the two spheres:
- To find how many times larger the surface area of sphere B is in comparison to sphere A, we divide the surface area of sphere B by the surface area of sphere A:
\[
\text{Ratio} = \frac{S_B}{S_A} = \frac{2304\pi}{144\pi} = \frac{2304}{144} = 16
\]
Thus, sphere B's surface area is 16 times as large as sphere A's.
Therefore, the correct comparison is:
**Sphere A has a surface area of \( 144\pi \, \text{in}^2 \) and sphere B has a surface area of \( 2304\pi \, \text{in}^2 \). This means that sphere B's surface area is 16 times as large as sphere A's.**
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