1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kherson [118]
3 years ago
8

Suppose that a balloon is being filled with air at a rate of 10 cm3/s. (Assume that theballoon is a perfect sphere.) At what rat

e is the surface area of the balloon changing when the radiusis 5 cm?
Physics
1 answer:
Basile [38]3 years ago
5 0

Answer:

Therefore the surface area of the balloon is increased at 4 cm³/s.

Explanation:

The balloon is being filled with air at a rate of 10 cm³/s

It means the volume of the balloon is increased at a rate 10 cm³/s.

i.e \frac{dv}{dt} =10 cm^3/s

Consider r be the radius of the balloon.

The volume of of a sphere is

v=\frac{4}{3} \pi r^3

Differentiate with respect to t

\frac{dv}{dt} =\frac{4}{3} \pi \times 3r^2\frac{dr}{dt}

\Rightarrow 10 =4\pi r^2\frac{dr}{dt}

\Rightarrow \frac{dr}{dt}=\frac{10}{4\pi r^2}

The surface of area of the balloon is(S) = 4\pi r^2

S=4\pi r^2

Differentiate with respect to t

\frac{dS}{dt} =4\pi\times2r\frac{dr}{dt}

\Rightarrow \frac{dS}{dt} =8\pi r\frac{dr}{dt}

Putting the value of \frac{dr}{dt}

\Rightarrow \frac{dS}{dt} =8\pi r\times\frac{10}{4\pi r^2}

\Rightarrow \frac{dS}{dt} =\frac{20}{ r}

Given that r = 5 cm

[\frac{dS}{dt}]_{r=5} =\frac{20}{ 5}  =4 cm³/s

Therefore the surface area of the balloon is increased at 4 cm³/s.

You might be interested in
A power supply is connected to a 59 Ohm resistor and a 53 Ohm resistor in series. The total current is found to be 0.15 A. What
kirill [66]

the answer is 47265.dug

Explanation:

im bot sure

4 0
2 years ago
Explain what is happening in this picture
Assoli18 [71]

Answer:

in this video waves are coming up for the BOTTOM to the top of the sandbar

7 0
3 years ago
A 20 g sparrow flying toward a bird feeder mistakes the pane of glass in a window for an opening and slams into it with a force
Rama09 [41]
I found this using the app Socratic. When I took physics in high school it helped me so much.

5 0
3 years ago
A 1000-turn solenoid is 50 cm long and has a radius of 2.0 cm. It carries a current of 18.0 A. What is the magnetic field inside
vitfil [10]

Answer:

The value  is  B =  0.0452 \  T

Explanation:

From the question we are told that

   The number of turns is  N  =  1000

    The length is  L =  50 cm =  0.50 m  

    The radius is  r =  2.0 cm  =  0.02 m

     The current is I  =  18.0 A

   

Generally the magnetic field is mathematically represented as

         B = \mu_o  * \frac{N }{L}  *  I

Here \mu_o is the permeability of free space with value  

     \mu_o  =  4\pi * 10^{-7} N/A^2

So

     B =  4\pi * 10^{-7}  *   \frac{1000}{0.50} *  18.0

=>   B =  0.0452 \  T

3 0
3 years ago
Several glands add fluids to the sperm to form semen as it passes through the vas deferens. true or false?
xenn [34]
The answer is true. It tells me I have to have 20 characters.
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the electric potential of a 2.2 µC charge at a distance of 6.3 m from the charge? Recall that Coulomb’s constant is k =
    12·2 answers
  • A fox sees a piece of carrion men thrown from a Hawk's Nest and rushes to snatch it. The best is 14.0m high and the carrion is t
    15·1 answer
  • A moving object with a decreasing velocity covers distance during
    15·1 answer
  • How do amplitude and frequency affect light energy? help asap !!!!!!
    14·1 answer
  • Which of the following is an inorganic compound?
    9·2 answers
  • How did the Planck mission help scientists learn about the age of the universe
    8·1 answer
  • Answer all these questions for a TON OF POINTS
    11·2 answers
  • Two resistors, A and B, are connected in a series circuit with a battery. The resistance of A is twice that of B. Which resistor
    9·1 answer
  • Do you divide mass by volume to get density
    12·1 answer
  • Rate of work done against water resistant? Can someone explain why its 3.0W? Thanks.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!