Q. 53.7( 3 Votes )

# If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere.

Answer :

Given the error in the measurement of the radius of a sphere is 0.1%.

Let x be the radius of the sphere and Δx be the error in the value of x.

Hence, we have

∴ Δx = 0.001x

The volume of a sphere of radius x is given by

On differentiating V with respect to x, we get

We know

Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as

Here, and Δx = 0.001x

⇒ ΔV = (4πx^{2})(0.001x)

∴ ΔV = 0.004πx^{3}

The percentage error is,

⇒ Error = 0.003 × 100%

∴ Error = 0.3%

Thus, the error in calculating the volume of the sphere is 0.3%.

Rate this question :

If y = sin x and x changes from to, what is the approximate change in y?

RD Sharma - Volume 1Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of the edges of the cube.

RD Sharma - Volume 1The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.

RD Sharma - Volume 1