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
Scorpion4ik [409]
3 years ago
9

The radius of the base of a cylinder is increasing at a rate of 7 millimeters per hour. The height of the cylinder is fixed at 1

.51, point, 5 millimeters. At a certain instant, the radius is 12 millimeters.
What is the rate of change of the volume of the cylinder at that instant (in cubic millimeters per hour)?
Mathematics
1 answer:
Ilya [14]3 years ago
6 0

Answer:

The rate of change of the volume of the cylinder at that instant = 791.28\ mm^3/hr

Step-by-step explanation:

Given:

Rate of increase of base of radius of base of cylinder = 7 mm/hr

Height of cylinder = 1.5 mm

Radius at a certain instant = 12 mm

To find rate of change of volume of cylinder at that instant.

Solution:

Let r represent radius of base of cylinder at any instant.

Rate of increase of base of radius of base of cylinder can be given as:

\frac{dr}{dt}=7\ mm/hr

Volume of cylinder is given by:

V=\pi\ r^2h

Finding derivative of the Volume with respect to time.

\frac{dV}{dt}=\pi\ h\ 2r\frac{dr}{dt}

Plugging in the values given:

\frac{dV}{dt}=\pi\ (1.5)\ 2(12)(7)

\frac{dV}{dt}=252\pi

Using \pi=3.14

\frac{dV}{dt}=252(3.14)

\frac{dV}{dt}=791.28\ mm^3/hr (Answer)

Thus rate of change of the volume of the cylinder at that instant = 791.28\ mm^3/hr

You might be interested in
Unit rate for typing 34 words in a minute in a half
katrin [286]

Answer:

<u>R</u><u>a</u><u>t</u><u>e</u><u> </u><u>i</u><u>s</u><u> </u><u>1</u><u>.</u><u>1</u><u>3</u><u>3</u><u>3</u><u> </u><u>w</u><u>o</u><u>r</u><u>d</u><u>s</u><u> </u><u>p</u><u>e</u><u>r</u><u> </u><u>s</u><u>e</u><u>c</u><u>o</u><u>n</u><u>d</u><u> </u>

Step-by-step explanation:

We understand rating as frequency or speed of doing something per time (seconds mainly)

{ \green{ \tt{rate = \frac{item \: quantity}{time}  }}} \\

Let's find rate in terms of seconds (words per second)

{ \rm{rate =  \frac{34 \: words}{ (\frac{1}{2} \times 60)  \: seconds} }} \\  \\ { \rm{rate =  \frac{34}{30} }} \\  \\ { \rm{rate = 1.133 \:  \: words \: per \: second}}

6 0
2 years ago
If a and b are independent events then it must be true that P(A|B)=P(A). TRUE OR FALSE.
Vesnalui [34]
This would be true because it shows that p equals either a or b and it also shows that p equals a which is true because it is one of the independent choices.
6 0
3 years ago
Read 2 more answers
What is the square footage of a area 20 feet by 50 feet
Westkost [7]
The footage is 1000 square footage
5 0
3 years ago
Read 2 more answers
12x+40=15x+25 solve for x
fiasKO [112]

Answer:

5 = x

Step-by-step explanation:

12x+40=15x+25

Subtract 12x from each side

12x-12x+40=15x-12x+25

40 = 3x +25

Subtract 25 from each side

40-25 = 3x+25-25

15 =3x

Divide by 3

15/3 =3x/3

5 = x

6 0
3 years ago
Read 2 more answers
Quadrilateral A and B are scaled copies of each other. Quadrilateral A has side lengths of 2, 3, 5, and 6. Quadrilateral B's lon
harkovskaia [24]

Answer:

Quadrilateral A has side lengths 2, 3, 5, and 6. Quadrilateral B has side lengths 4, 5, 8, and 10. Could one of the quadrilaterals be a scaled copy of the other ...

4 0
3 years ago
Other questions:
  • If a total of 30 cups of mangoes and blueberries are used, how many batches of the recipe did the chef make
    10·1 answer
  • A number is multiplied by 5 then 3 is subtracted from the product the result is 12
    9·2 answers
  • If m&lt;PQT=60 and m&lt;PQS=4x+14 find the value if x
    9·1 answer
  • 65 points!!!!
    8·2 answers
  • The total cost (c) in dollars of renting a car for n days is given by the inequality LaTeX: c\ge125+50nc ≥ 125 + 50 n. What is t
    5·1 answer
  • Factor using x method and foil to prove
    15·1 answer
  • PLEASE HELP which number line represents the solution to |x-5|&lt; 3 ?
    15·1 answer
  • 7 less than the square of a number.
    8·1 answer
  • Can someone check if this is right or did I solve it wrong?
    13·1 answer
  • Find the domain and range with a vertex of (1,-2)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!