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Firdavs [7]
3 years ago
10

The volume of a cone of radius r and height h is given by V=πr²h³. If the radius and the height both increase at a constant rate

of 12 cms/sec, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?
Mathematics
1 answer:
Aloiza [94]3 years ago
5 0

Answer:

The volume of cone is increasing at a rate 1808.64 cubic cm per second.

Step-by-step explanation:

We are given the following in the question:

\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}

Volume of cone =

V = \dfrac{1}{3}\pi r^2 h

where r is the radius and h is the height of the cone.

Instant height = 9 cm

Instant radius = 6 cm

Rate of change of volume =

\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})

Putting values, we get,

\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}

Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.

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Can someone help me with these
Trava [24]
Short answer
For 6: 72 ft^2
For 7: 650 m^2

Six
The base is a square. It's measurement is s = 4
Base = 4^2 
Base = 16 ft^2

One triangle 
A = 1/2 * b * h
A = 1/2 * 4 * 7
A = 14 tt^2

Four triangles
A = 4 * 14
A = 56 ft^2

Total Area = 56 + 16 = 72 ft^2
Answer 72 square feet

Seven
Triangles
Area of 1 triangle = 1/2 * 10 * 13
Area of 1 triangle = 65


Area of 6 triangles
Area of 6 triangles = 6 * area of 1 triangle
Area of 6 triangles = 390

Base
As near as I can tell, the base is a hexagon. It's using a rather out of the way method of drawing it. I will assume it is a regular hexagon. The area of a regular hexagon is 3 sqrt(3)/2 * S^2 where s is the side of the hexagon.

Area = 3sqrt(3)/2 s^2
s = 10
Area = 3sqrt(3)/2 10^2
Area = 5.1962 * 100 /2
Area = 259.81

Total area
Total area = area of the base + area of the triangles
Total area = 259.81 + 390
Total area (rounded ) = 650

Answer C <<<< answer 

I'll do one more in this batch and then you'll need to repost again.

Eight

If you draw two diagonals on the base of the figure, the intersection point will meet the base of the height. Read that a couple of times.
Join the intersection to the midpoint of the length of the square bottom.  You should get 3.5

x is found by using the pythagorean theorem.
h = 6
s = 3.5
x = ????

x^2 = 6^2 + 3.5^2
x^2 = 36 + 12.25
x^2 = 48.25
x = sqrt(48.25)
x = 6.95 

C <<<< answer

 


8 0
3 years ago
Evaluate 21/a+4 when a=3
DochEvi [55]

Answer:

11

Step-by-step explanation:

All you have to do is plug in a. In this case, a=3.

21/a+4

21/(3)+4

21/3+4

7+4

11

If this helps please mark as brainliest

5 0
2 years ago
Read 2 more answers
Jeremiah always rides his bike to and from work. The total
Katen [24]

From the computation done, the total kilometers that he uses last month will be 262.8 kilometers.

The total length of a trip to and from work is 14.6 kilometers and last month, Jeremiah worked 18 days.

Therefore, the kilometers that he rode his bike to and from work last month will be;

= 14.6 × 18.

= 262.8 kilometers.

Learn more about equations on:

brainly.com/question/13763238

7 0
2 years ago
The ratio of red cars to blue cars in a parking lot was 5:3 . If there was 40 red cars , how many blue cars were there ?
Bas_tet [7]
The answer is x equals 24
you set up a proportion new over old
so for red cars 40 over 5
since we don’t know the new for blue cars we’ll use x
so x over 3
we then make them equal to each other
40 x
—- = —-
5 3
cross multiply, then we get
120=5x
isolate the x by dividing 5 from both sides to get 24
5 0
3 years ago
Calculate 32 percent of 133
Rasek [7]
0.32 x 133
=42.56
:) hope that helps
3 0
3 years ago
Read 2 more answers
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