The radius of a sphere increases at a rate of 4m/\sec. Find the rate at which the surface area increases when the radius is 9m. 288\pi m^{2}/\sec 36\pi m^{2}/\sec 18\pi m^{2}/\sec 72\pi m^{2}/\sec 144\pi m^{2}/\sec

asked 2021-05-04
The radius of a sphere increases at a rate of \(4m/\sec\). Find the rate at which the surface area increases when the radius is 9m.
\(288\pi m^{2}/\sec\)
\(36\pi m^{2}/\sec\)
\(18\pi m^{2}/\sec\)
\(72\pi m^{2}/\sec\)
\(144\pi m^{2}/\sec\)

Answers (1)

Step 1
Surface area of sphere is \(S= 4\pi r^{2}\).
And rate of change means derivatives.
Step 2
Now let radius of sphere is =r.
So dr/dt=4.
So rate of change of surface area \(= dS/dt= 8\pi r.dr/dt =8\pi .9.4=288\pi\).
So options A correct.
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-03-22
A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant but starts at .100 at P and increases linerly with distance past P, reaching a value of .600 at 12.5 m past point P. (a) Use the work energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid iff the friciton coefficient didn't increase, but instead had the constant value of .1?
asked 2021-02-23
A 0.30 kg ladle sliding on a horizontal frictionless surface isattached to one end of a horizontal spring (k = 500 N/m) whoseother end is fixed. The ladle has a kinetic energy of 10 J as itpasses through its equilibrium position (the point at which thespring force is zero).
(a) At what rate is the spring doing work on the ladle as the ladlepasses through its equilibrium position?
(b) At what rate is the spring doing work on the ladle when thespring is compressed 0.10 m and the ladle is moving away from theequilibrium position?
asked 2021-04-06
A race car enters a flat 200 m radius curve at a speed of 20 m/swhile increasing its speed at a constant 2 m/s2. If the coefficient of static friction is .700, what will the speed of thecar be when the car beings to slide?
A) 24.3 m/s
B) 31.5 m/s
C) 37.1 m/s
D) 36.2 m/s
E) 28.7 m/s
asked 2021-06-09
Change from rectangular to cylindrical coordinates. (Let \(r\geq0\) and \(0\leq\theta\leq2\pi\).)
a) \((-2, 2, 2)\)
b) \((-9,9\sqrt{3,6})\)
c) Use cylindrical coordinates.
where E is enclosed by the planes \(z=0\) and
and by the cylinders
\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)
d) Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
and the sphere
asked 2021-02-19
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
asked 2020-12-12

Show that at the bottom of a vertical mine shaft dug to depthD, the measured value of ag will be \(ag = a_{gs}(1 - D/R)\), \(a_{gs}\) being the surface value. Assume that Earth is a uniform sphere of radius R.

asked 2021-04-23
To monitor the breathing of a hospital patient, a thin belt isgirded around the patient's chest. The belt is a200-turn coil. When the patient inhales, the area encircled by the coil increases by \(\displaystyle{39.0}{c}{m}^{{2}}\). The magnitude of the Earth's magnetic field is 50.0uT and makes an angle of 28.0 degree with the plane of the coil. Assuming a patien takes 1.80s toin hale, find the magnitude of the average induced emf in the coilduring that time.
Do I use the equation \(\displaystyle{E}={N}\cdot{A}\cdot{B}{w}{\sin{{w}}}{t}\)?
asked 2021-06-14
A wheel with a 30-cm radius is rotating at a rate of 3 radians/sec. What is the linear speed of a point on its rim, in meters per minute?
asked 2021-03-27
Water is being boiled in an open kettle that has a 0.500-cm-thick circular aluminum bottle with a radius of 12.0cm. If the water boils away at a rate of 0.500 kg/min,what is the temperature of the lower surface of the bottom of the kettle? Assume that the top surface of the bottom of the kettle is at \(\displaystyle{100}^{\circ}\) C.
asked 2021-02-23
Solid NaBr is slowly added to a solution that is 0.010 M inCu+ and 0.010 M in Ag+. (a) Which compoundwill begin to precipitate first? (b) Calculate [Ag+] when CuBr justbegins to precipitate. (c) What percent of Ag+ remains in solutionat this point?
a) AgBr: \(\displaystyle{\left({0.010}+{s}\right)}{s}={4.2}\cdot{10}^{{-{8}}}\) \(\displaystyle{s}={4.2}\cdot{10}^{{-{9}}}{M}{B}{r}\) needed form PPT
CuBr: \(\displaystyle{\left({0.010}+{s}\right)}{s}={7.7}\cdot{\left({0.010}+{s}\right)}{s}={7.7}\cdot{10}^{{-{13}}}\) Ag+=\(\displaystyle{1.8}\cdot{10}^{{-{7}}}\)
b) \(\displaystyle{4.2}\cdot{10}^{{-{6}}}{\left[{A}{g}+\right]}={7.7}\cdot{10}^{{-{13}}}\) [Ag+]\(\displaystyle={1.8}\cdot{10}^{{-{7}}}\)
c) \(\displaystyle{\frac{{{1.8}\cdot{10}^{{-{7}}}}}{{{0.010}{M}}}}\cdot{100}\%={0.18}\%\)