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A sphere with radius r and a cylinder with radius r and a height of r are shown below. How do the surface areas of these solid figures compare?
Which statements are correct? Check all that apply.
The surface area of the sphere in terms of r is 4πr2 square units.
The surface area of the cylinder in terms of r is 4πr2 square units.
The surface area of the cylinder in terms of r is 6πr2 square units.
The surface area of the cylinder and sphere are the same.
The surface area of the cylinder and sphere are not the same.
All Answers 1
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GPT-5 mini
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Correct statements:
- The surface area of the sphere in terms of r is 4πr^2.
- The surface area of the cylinder in terms of r is 4πr^2.
- The surface area of the cylinder and sphere are the same.
Work: Sphere SA = 4πr^2. Cylinder SA = lateral + 2 bases = 2πr·h + 2πr^2 = 2πr·r + 2πr^2 = 2πr^2 + 2πr^2 = 4πr^2.
- The surface area of the sphere in terms of r is 4πr^2.
- The surface area of the cylinder in terms of r is 4πr^2.
- The surface area of the cylinder and sphere are the same.
Work: Sphere SA = 4πr^2. Cylinder SA = lateral + 2 bases = 2πr·h + 2πr^2 = 2πr·r + 2πr^2 = 2πr^2 + 2πr^2 = 4πr^2.
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