Question

The radius of a closed cylinder is half of its height . If an error of 0.5% is made in measuring the radius , the percentage error in the surface area is

Answer 1

Let. The. Radius be r units. Then heightof the cylinder will be 2r units

Measured. Length of. Radius

is. 0.5/100*r. Units less so,

Length. Measured is r-0.5/100*r=0.995r

Actual surface area of cylinder is. 2π(r)(2r)

Measured surface area of cylinder is 2π(o.995r)(2)0.995r

So,

Persantage error in. Measuring is

2π(0.995r)(2)(o.995r)/2π(r)(2r)*100=99.0025

So. Error persentage. Is. 100-99.0025=0.9975

So. Persentage error. Is 0.9975%

Answer 2

Answer:

Percentage error in the surface area of cylinder is 1%.

Step-by-step explanation:

Given the radius of a closed cylinder is equal half of its height.

Error in measurement of radius is 0.5%

$\implies \frac{dr}{r}\times 100 =0.5$

Let the radius of the cylinder be r units.

Then height of the cylinder,  $h= 2r units$

Surface area of cylinder, $A=2\pi r(r+h)$

$=2\pi r(r+2r)=6\pi r^{2}$

Differentiating the surface area with respect to radius,

$\frac{dA}{dr} =\frac{d}{dr} (6\pi r^{2} )=12\pi r$

$dA =12\pi rdr$

Dividing with the surface area of cylinder

$\frac{dA}{A} =\frac{12\pi rdr}{6\pi r^{2} }$  

Multiplying with 100 on both sides

$\frac{dA}{A}\times 100 =\frac{2dr}{r }\times 100$  

$\frac{dA}{A}\times 100 =2\times 0.5=1\%$

Therefore, percentage error in the surface area is 1%.