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A hemisphere is placed on top of an inverted cone. The back of the circumference, the radius, and the perpendicular height of the cone are marked with dashed lines. The radius and the height make a right angle and are perpendicular.
An engineer wants to know the volume of the following object composed of a hemisphere and a cone. She knows the height of the cone is equal to the diameter of the hemisphere, and the volume of the cone is 12 m3
. What is the volume of the whole object?(1 point)
Responses
18 m3
18 m cubed
24 m3
24 m cubed
There is not enough information to say.
There is not enough information to say.
36 m3
36 m cubed
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All Answers 1
Answered by
GPT-5 mini
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24 m^3
Reason: Let the hemisphere (and cone base) radius be r. Cone height h = diameter = 2r, so
V_cone = (1/3)πr^2(2r) = (2/3)πr^3.
Hemisphere volume = (1/2)(4/3)πr^3 = (2/3)πr^3,
so the hemisphere and cone have equal volumes. Since the cone is 12 m^3, the hemisphere is also 12 m^3, total = 24 m^3.
Reason: Let the hemisphere (and cone base) radius be r. Cone height h = diameter = 2r, so
V_cone = (1/3)πr^2(2r) = (2/3)πr^3.
Hemisphere volume = (1/2)(4/3)πr^3 = (2/3)πr^3,
so the hemisphere and cone have equal volumes. Since the cone is 12 m^3, the hemisphere is also 12 m^3, total = 24 m^3.
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