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likoan [24]
3 years ago
14

A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone i

s equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r? What is the ratio of the radius of a circle to its circumference?
Mathematics
2 answers:
kondaur [170]3 years ago
4 0
Given:
Volume of the cone = π r² h/3

radius of the cone is half the radius of the cylinder ⇒ r/2
height of the cone is equal to the radius of the cylinder. ⇒ r

V = 3.14 * (r/2)² * r/3
V = 3.14 * r²/4 * r/3
V = 3.14r³ / 12

Ivanshal [37]3 years ago
3 0

Answer:


C.   V = \frac{1}{12} π r^{3}

Step-by-step explanation:

<em>A. </em><em>  V = \frac{1}{3} π r^{2} h</em>


B.  V = \frac{1}{6} π r^{2}


C.   V = \frac{1}{12} π r^{3}


D.   V = 2 π r^{3}

<em>π Is Meant To be </em><em>π</em>

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Answer:

x  =  7

y  =  3

z (max)  =  4950/3  =  1650

Step-by-step explanation:

Let call  

x numbers of church goup and

y numbers of Union Local

Then  

First contraint

2*x + 2*y ≤ 20

Second one

1*x + 3*y ≤ 16

Objective Function

z = 150*x + 200*y

Then the system is

z = 150*x + 200*y To maximize

Subject to:

2*x + 2*y ≤ 20

1*x + 3*y ≤ 16

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We will solve by using the Simplex method

z - 150 *x - 200*y = 0

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First Table

z           x          y          s₁           s₂          Cte

1        -150    -200       0            0     =      0

0          2         2           1            0     =    20

0          1          3          0            1      =     16

First iteration:

Column pivot   ( y column ) row pivot (third row) pivot 3

Second table

z           x                y          s₁           s₂                Cte

1       -250/3           0          0         200/3    =    3200/3

0      - 4/3               0          -1           2/3       =    -20/3

0         1/3               1            0           1/3       =    -20/3

Second iteration:

Column pivot  ( x column ) row pivot  (second row)  pivot  -4/3

Third table

z           x                y          s₁           s₂                Cte

1            0               0      750/12    700/6    =   4950/3

0            1                0        3/4          -1/2     =    7

0            0                1         -1/4          1/2     =  9/3

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Answer:

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The graph passed through above points.

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