55966
AssignmentMultiple Select

Spheres

Question 55966 • Reading HS- Integrated Math I

A glass dome for a lighting fixture is in the shape of a hemisphere. The circumference of the great circle of the hemisphere is 12π inches. Which statements about the hemisphere are true? Check all that apply.The radius is 6 inches.The total surface area is 108π square inches.The radius is 12 inches.The total surface area is 144π square inches.The total surface area is 432π square inches.The total surface area is 36π square inches.

Answer
A
The radius is 6 inches.
B
The total surface area is 108π square inches.
C
The radius is 12 inches.
D
The total surface area is 144π square inches.
E
The total surface area is 432π square inches.
F
The total surface area is 36π square inches.

Explanation

The great-circle circumference is 2πr, so 2πr = 12π gives a radius of 6 inches. A hemisphere’s total surface area includes its curved surface and circular base, so it is 3πr² = 3π(6²) = 108π square inches. Therefore, the true statements are that the radius is 6 inches and the total surface area is 108π square inches.

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