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If the height of the cone is 5 cm and the volume is 500 cm^3, what is the radius of the cone?
(1 point)
The radius is the same as a cylinder with a volume of 500/3 and the same height.
The radius is the same as a cylinder with the same volume and same height.
The radius is the same as a cylinder with the same volume and height of 3.
The radius is the same as a cylinder with a volume 500(3) and same height.
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GPT-5 mini
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Correct answer: "The radius is the same as a cylinder with a volume 500(3) and same height." (option 4)
Reason: Vcone = (1/3)πr^2h, so a cylinder with the same r and h has volume 3Vcone = 1500 cm^3. Solving 500 = (1/3)πr^2(5) gives r^2 = 300/π, so r = sqrt(300/π) ≈ 9.77 cm.
Reason: Vcone = (1/3)πr^2h, so a cylinder with the same r and h has volume 3Vcone = 1500 cm^3. Solving 500 = (1/3)πr^2(5) gives r^2 = 300/π, so r = sqrt(300/π) ≈ 9.77 cm.
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