Advertisements
Advertisements
Question
Find the approximate change in the volume V of a cube of side x metres caused by increasing side by 1%.
Advertisements
Solution
The volume of a cube (V) of side x is given by V = x3.

Hence, the approximate change in the volume of the cube is 0.03x3 m3.
APPEARS IN
RELATED QUESTIONS
Find the approximate value of cos (60° 30').
(Given: 1° = 0.0175c, sin 60° = 0.8660)
Using differentials, find the approximate value of the following up to 3 places of decimal
`(401)^(1/2)`
Using differentials, find the approximate value of the following up to 3 places of decimal
`(81.5)^(1/4)`
Show that the function given by `f(x) = (log x)/x` has maximum at x = e.
The normal at the point (1, 1) on the curve 2y + x2 = 3 is
(A) x + y = 0
(B) x − y = 0
(C) x + y + 1 = 0
(D) x − y = 1
The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?
A circular metal plate expends under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.
Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?
Using differentials, find the approximate values of the cos 61°, it being given that sin60° = 0.86603 and 1° = 0.01745 radian ?
Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?
Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?
Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?
Using differential, find the approximate value of the \[{25}^\frac{1}{3}\] ?
If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area ?
If the radius of a sphere is measured as 7 m with an error of 0.02 m, find the approximate error in calculating its volume ?
Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1% ?
For the function y = x2, if x = 10 and ∆x = 0.1. Find ∆ y ?
If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?
A piece of ice is in the form of a cube melts so that the percentage error in the edge of cube is a, then find the percentage error in its volume ?
While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is
A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is λ %, then the error in its volume is
The pressure P and volume V of a gas are connected by the relation PV1/4 = constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the volume is
The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is
Find the approximate value of f(3.02), up to 2 places of decimal, where f(x) = 3x2 + 5x + 3.
Find the approximate values of : (3.97)4
Find the approximate values of : sin 61° , given that 1° = 0.0174c, `sqrt(3) = 1.732`
Find the approximate values of : 32.01, given that log 3 = 1.0986
Find the approximate values of : loge(9.01), given that log 3 = 1.0986.
The approximate value of the function f(x) = x3 − 3x + 5 at x = 1.99 is ____________.
Find the approximate value of (1.999)5.
If the radius of a sphere is measured as 9 m with an error of 0.03 m. the find the approximate error in calculating its surface area
Find the approximate value of sin (30° 30′). Give that 1° = 0.0175c and cos 30° = 0.866
