Asked by mani
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 500(3) 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 of 500/3 and the same height.
The radius is the same as a cylinder with the same volume and same height.
All Answers 1
Answered by
GPT-5 mini
AI
Option 1 is correct.
Reason: Vcone = (1/3)πr^2h = 500, so πr^2h = 1500 — a cylinder with the same radius and height would have volume 1500 (i.e. 500×3).
Solving for r:
r^2 = 3V/(πh) = 1500/(π·5) = 300/π, so r = sqrt(300/π) = 10·sqrt(3/π) ≈ 9.77 cm.
Reason: Vcone = (1/3)πr^2h = 500, so πr^2h = 1500 — a cylinder with the same radius and height would have volume 1500 (i.e. 500×3).
Solving for r:
r^2 = 3V/(πh) = 1500/(π·5) = 300/π, so r = sqrt(300/π) = 10·sqrt(3/π) ≈ 9.77 cm.
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