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Nonamiya [84]
3 years ago
8

A concrete pillar has the shape of a cylinder. It has a radius of 3 m and a height of 7 m. If concrete cost $116 per cubic meter

how much did the concrete cost for the pillar?
Mathematics
2 answers:
brilliants [131]3 years ago
8 0

Answer: the concrete cost for the pillar is $22947.12

Step-by-step explanation:

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

The cylindrical concrete pillar has has a radius of 3 m and a height of 7 m. Therefore, the volume of concrete cylinder would be

Volume = 3.14 × 3² × 7 = 197.82 cubic meter

If concrete cost $116 per cubic meter, the cost of the concrete would be

116 × 197.82

= $22947.12

Olin [163]3 years ago
7 0

Answer:

$22,968

Step-by-step explanation:

To solve this question, we need to find the volume of the cylinder. Let’s call this V

Mathematically V = πr2h

where r = 3m , h = 7m and π = 22/7

Putting this in the formula:

V = 22/7 * 3 * 3 * 7 = 198 cubic meter

We are told concrete costs $116 per cubic meter. Hence, for 198 cubic meter we have 198 * 116 = $22,968

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Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat
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Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

<u>Step 1</u>:-

Given volume of the largest rectangular box in the first octant

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<u>Step( ii):</u>

By using  Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ  Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

                                  δ f / δ x +λ  δ Ф  / δ x =0

                           ⇒ y z + λ ( 1) = 0

                          ⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

                            δ f / δ x +λ  δ Ф  / δ x =0

                        ⇒ x z + λ ( 9) = 0

                        ⇒ \frac{xz}{9} = - λ .......(b)

Obtain the equations are δ F / δ z = 0

                                  δ f / δ x +λ  δ Ф  / δ z =0

                                   x y + λ ( 4) = 0

                                    ⇒ \frac{xy}{4} = - λ .......(c)

<u>Step (iii):-</u>

Equating (a) and (b) equations

we get         y z = \frac{xz}{9}

cancel 'z' value we get  x = 9y  .......(d)

Equating (b) and (c) equations

we get     \frac{xy}{4}  = \frac{xz}{9}

cancel 'x' value on both sides , we get

              4z =9y  ......(e)

substitute (d) (e) values in equation (1)  we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

27y -27 =0

<u> y = 1</u>

substitute y =1 in x = 9y

<u>x = 9</u>

substitute y =1 in 4z =9y

<u>z = 9 /4</u>

therefore the dimensions are x =9 , y=1 and z = 9 /4

<u>Conclusion</u>:-

The largest volume of the rectangular box V = x y z

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

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substitute x =9 , y=1 and z = 9 /4

              9 + 9 + 4(9/4) = 27

           27 =27

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