Answer:
6%
Step-by-step explanation:
Since the volume of the cylinder V = πr²h where r = radius of cylinder and h = height of cylinder and h = 2r, we have that r = h/2.
Substituting r into v, we have
V = πr²h
V = π(h/2)²h
V = πh³/4
Now let ΔV be the error in the volume and Δh be the error in the height.
Since h is raised to the power of 3,
ΔV/V = 3Δh/h
multiplying both sides by 100, we have
ΔV/V × 100 = 3Δh/h × 100
So, we have
ΔV/V × 100 = 3 × Δh/h × 100
since Δh/h × 100 = percentage error in height = 2%, and ΔV/V × 100 = percentage error in volume,
ΔV/V × 100 = 3 × 2% = 6%
So, the percentage error in volume is 6 %
