Question

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.

Answer 1

i think I don't know

Answer 2

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