Loading [MathJax]/jax/output/HTML-CSS/jax.js

Home / Aptitude Tests / Mathematics / The area A of a circ...

The area A of a circle is increasing at a constant rate of 1...

The area A of a circle is increasing at a constant rate of 1.5 cm $^2s^{-1}$ . Find, to 3 significant figures, the rate at which the radius r of the circle is increasing when the area of the circle is 2 cm $^2$ .

A.

0.200 cms $^{-1}$

B.

0.798 cms $^{-1}$

C.

0.300 cms $^{-1}$

D.

0.299 cms $^{-1}$

View answer & explanation

Correct answer is D

Area of a circle (A) = $\pi r^2$

Given

$\frac{dA}{dt} = 1.5cm^2s^{-1}$

$\frac{dr}{dt}$ = ?

A = 2cm $^2$

Now

2 = $\pi r^2$

= r $^2 = \frac {2}{\pi}$

r = $\sqrt \frac {2}{\pi}$ cm = 0.798cm

$\frac {dr}{dt} = \frac {dA}{dt} \times \frac {dr}{dt}$

$\frac {dA}{dr} = 2\pi r$ (differentiating A = $\pi r^2)$

$\frac {dr}{dA} = \frac {1}{2\pi r}$

$\frac {dr}{dt} = 1.5 \times \frac {1}{2\times \pi \times 0.798} = 1.5 \times 0.199$

$\frac {dr}{dt} = 0.299cms^{-1}$ (to 3 s.f)

See all Mathematics questions & answers

See more JAMB questions & answers

Similar Questions

Form an inequality for a distance d meters which is more than 18m, but not more than 23m ...

Find the quadratic equation whose roots are x = -2 or x = 7 ...

The graph represents the relation y = x $^2$ - 3x - 3. What is the equation of the line of symmetry...

In the diagram above, O is the center of the circle and ∠POR = 126°. Find ∠PQR ...

Two triangles have the same areas if ...

Esther was facing S 20° W. She turned 90° in the clock wise direction. What direction is she facin...

5, 8, 6 and k occur with frequency 3, 2, 4, and 1 respectively and have a mean of 5.7. Find the valu...

The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is ...

If x + 0.4y = 3 and y = $\frac{1}{2}$ x, find the value of (x + y)...

Evaluate: (0.064) - $\frac{1}{3}$ ...

Aptitude Tests

Typing Speed and Accuracy Test

Situational Judgement Questions and Answers

Nigeria General Knowledge Questions and Answers

Quantitative Reasoning Questions and Answers

Microsoft Office Questions and Answers

Numerical Reasoning Questions and Answers

Logical Reasoning Questions and Answers

Data Interpretation Questions and Answers

Puzzles Questions and Answers

Spatial Reasoning Questions and Answers

Personality Test

Verbal Reasoning Questions and Answers

Abstract Reasoning Questions and Answers

View latest jobs in Nigeria today