Advertisements
Advertisements
प्रश्न
A circular plate expands uniformly under the influence of heat. If its radius increases from 10.5 cm to 10.75 cm, then find an approximate change in the area and the approximate percentage change in the area
Advertisements
उत्तर
Area of the circular plate A = πr2
= π × 10.5 × 105
= 110.25π
dA = 2πrdr
= 2π × 10.5 × 0.251
= 5.25π
Approximate percentage change in the area
= `"dA"/"A" xx 100`
= `(5.25pi)/(110.25pi) xx 100`
= 0.04761 × 100
= 4.76%
APPEARS IN
संबंधित प्रश्न
Use the linear approximation to find approximate values of `(123)^(2/3)`
Use the linear approximation to find approximate values of `root(3)(26)`
Find a linear approximation for the following functions at the indicated points.
f(x) = x3 – 5x + 12, x0 = 2
The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:
Relative error
The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:
Percentage error
Find the differential dy for the following functions:
y = `(1 - 2x)^3/(3 - 4x)`
Assuming log10 e = 0.4343, find an approximate value of Iog10 1003
The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. Approximately how much did the tree diameter grow?
The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. What is the percentage increase in the area of the cross-section of the tree?
Assume that the cross-section of the artery of human is circular. A drug is given to a patient to dilate his arteries. If the radius of an artery is increased from 2 mm to 2.1 mm, how much is cross-sectional area increased approximately?
In a newly developed city, it is estimated that the voting population (in thousands) will increase according to V(t) = 30 + 12t2 – t3, 0 ≤ t ≤ 8 where t is the time in years. Find the approximate change in voters for the time change from 4 to `4 1/6` years
The relation between the number of words y a person learns in x hours is given by y = `sqrt(x), 0 ≤ x ≤ 9`. What is the approximate number of words learned when x changes from 1 to 1.1 hours?
Choose the correct alternative:
A circular template has a radius of 10 cm. The measurement of the radius has an approximate error of 0.02 cm. Then the percentage error in the calculating the area of this template is
Choose the correct alternative:
The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?
Choose the correct alternative:
If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is
Choose the correct alternative:
The approximate change in volume V of a cube of side x meters caused by increasing the side by 1% is
Choose the correct alternative:
Linear approximation for g(x) = cos x at x = `pi/2` is
