Question

The volume of a circular cylinder is calculated using the formula

Answer 1

6%

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 %