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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 4in and sphere B which has a radius of 10 in. The formula for the surface area of a sphere is 4πr2
(1 point)
Responses
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 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 16π in2
and sphere B has a surface area of 40π in2
, meaning sphere B's surface area is 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 40π in2
, meaning sphere B's surface area is 5 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 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 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 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.
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(1 point)
Responses
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 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 16π in2
and sphere B has a surface area of 40π in2
, meaning sphere B's surface area is 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 40π in2
, meaning sphere B's surface area is 5 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 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 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 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.
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To calculate the surface area of each sphere, we will use the formula for the surface area of a sphere:
\[
\text{Surface Area} = 4\pi r^2
\]
**For Sphere A (radius = 4 inches):**
\[
\text{Surface Area of Sphere A} = 4\pi (4)^2 = 4\pi (16) = 64\pi \text{ in}^2
\]
**For Sphere B (radius = 10 inches):**
\[
\text{Surface Area of Sphere B} = 4\pi (10)^2 = 4\pi (100) = 400\pi \text{ in}^2
\]
Now, we can compare the surface areas:
\[
\frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25
\]
Thus, Sphere B's surface area is 6.25 times as large as Sphere A's.
**Final Results:**
- 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.
So the correct response is:
**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.**
\[
\text{Surface Area} = 4\pi r^2
\]
**For Sphere A (radius = 4 inches):**
\[
\text{Surface Area of Sphere A} = 4\pi (4)^2 = 4\pi (16) = 64\pi \text{ in}^2
\]
**For Sphere B (radius = 10 inches):**
\[
\text{Surface Area of Sphere B} = 4\pi (10)^2 = 4\pi (100) = 400\pi \text{ in}^2
\]
Now, we can compare the surface areas:
\[
\frac{\text{Surface Area of Sphere B}}{\text{Surface Area of Sphere A}} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25
\]
Thus, Sphere B's surface area is 6.25 times as large as Sphere A's.
**Final Results:**
- 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.
So the correct response is:
**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.**
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