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Scorpion4ik [409]
2 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]2 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

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Answer:

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$500 / 5 / 2 =           50 candles

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago
George had one sheet of paper. He cut it into 6" x 5", and 3" x 6". What were the dimensions and total area of his original shee
Deffense [45]

Answer:l={8}'' ,b={6}'',l={6}'' ,b={8}''

and area is=48 inch square

Step-by-step explanation:

area of sheet=l\times b

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=30 inch square

area of sheet second={3}''\times {6}''

=18 inch square

total area of both sheet=30+18

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area of sheet=l\times b

=48 inch square

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or

l={8}'' ,b={6}''

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={28}''

3 0
3 years ago
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Hannah is asked to convert the number 0.00000305 to scientific notation. Her answer is 3.05 × 106. Which statement best describe
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Nataly_w [17]

Answer:

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Step-by-step explanation:

If the glass were initially 4/7 full, that means 3/7 of the volume is still available to hold more juice.

Let v represent the volume of the glass.  

Then (3/7)v + 70 cm³ = (3/4)v.

We need to solve this for v.

Here the LCD is 28.  Thus,

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Subtracting  (12/28)v from both sides, we get:

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We can isolate v by mult. both sides by the inverse of 9/28, which is 28/9:

(28/9)(70 cm³) = v

The volume of the glass is 217.8 cm³

3 0
3 years ago
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