Advertisements
Advertisements
Question
The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is
Options
\[\frac{1}{14}\]
0.01
\[\frac{1}{7}\]
none of these
Advertisements
Solution
\[\frac{1}{14}\]
Let x be the radius of the circle and y be its circumference.
\[x = 28 cm\]
\[ ∆ x = 0 . 01 cm\]
\[x = 2\pi r\]
\[y = \pi r^2 = \pi \times \frac{x^2}{4 \pi^2} = \frac{x^2}{4\pi}\]
\[ \Rightarrow \frac{dy}{dx} = \frac{x}{2\pi}\]
\[ \Rightarrow \frac{∆ y}{y} = \frac{x}{2\pi y}dx = \frac{2}{x} \times 0 . 01\]
\[ \Rightarrow \frac{∆ y}{y} \times 100 = \frac{2}{x} = \frac{1}{14}\]
\[\text { Hence, the percentage error in the area is } \frac{1}{14} .\]
APPEARS IN
RELATED QUESTIONS
Using differentials, find the approximate value of the following up to 3 places of decimal
`sqrt(0.6)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(15)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(255)^(1/4)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(0.0037)^(1/2)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(26.57)^(1/3)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(81.5)^(1/4)`
The normal to the curve x2 = 4y passing (1, 2) is
(A) x + y = 3
(B) x − y = 3
(C) x + y = 1
(D) x − y = 1
Find the approximate change in the volume ‘V’ of a cube of side x metres caused by decreasing the side by 1%.
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 ?
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the loge 4.04, it being given that log104 = 0.6021 and log10e = 0.4343 ?
Using differential, find the approximate value of the loge 10.02, it being given that loge10 = 2.3026 ?
Using differential, find the approximate value of the log10 10.1, it being given that log10e = 0.4343 ?
Using differential, find the approximate value of the \[\cos\left( \frac{11\pi}{36} \right)\] ?
Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\sqrt{37}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?
Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?
Using differential, find the approximate value of the \[{25}^\frac{1}{3}\] ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
Find the approximate values of : `sqrt(8.95)`
Find the approximate values of: `root(3)(28)`
Find the approximate values of : cos(60° 30°), given that 1° = 0.0175°, `sqrt(3) = 1.732`
Find the approximate values of : e0.995, given that e = 2.7183.
Find the approximate values of : loge(101), given that loge10 = 2.3026.
Find the approximate values of : f(x) = x3 – 3x + 5 at x = 1.99.
Find the approximate value of the function f(x) = `sqrt(x^2 + 3x)` at x = 1.02.
If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.
If `(x) = 3x^2 + 15x + 5`, then the approximate value of `f(3.02)` is
The approximate change in volume of a cube of side `x` meters coverd by increasing the side by 3% is
The approximate value of f(x) = x3 + 5x2 – 7x + 9 at x = 1.1 is ______.
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
Find the approximate value of tan−1 (1.002).
[Given: π = 3.1416]
