If the radius of a cone is twice its height, find the approximate error in the calculation of its volume, when the radius is 10 cm and the error in the radius is 0.01 cm.
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i think I don't know
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Answer:
ΔV = 0.5π cm³
Step-by-step explanation:
radius of a cone is twice its height
=> height = 5 cm with 0.005 cm error
ΔV/V = 2 * Δr/r + Δh/h
=> ΔV/V = 2 * 0.01/10 + 0.005/5
=> ΔV/V = 3 * 0.001
=> ΔV = 0.003V
V = (1/3)π r²h
=> V = (1/3)π 10² * 5
=> V = 500π/3
ΔV = 0.003 * 500π/3
ΔV = 0.5π cm³
approximate error in the calculation of its volume = 0.5π cm³
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