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3 years ago

What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 2197 cm cubed?

Mathematics

1 answer:

Zarrin [17]3 years ago

4 0

Answer:

radius = height ≈ 8.88 cm

Step-by-step explanation:

If the weight is proportional to the surface area, then we need to find the minimum surface area for the given volume.

The volume of the can is given by ...

V = πr²h . . . . . . for radius r and height h

The surface area includes that of the bottom and the sides:

SA = πr² +2πrh

Solving the first equation for h, we can write the second equation as ...

SA = πr² +2πr(V/(πr²)) = πr² +2V/r

The minimum area for the volume will be found where the derivative is zero.

d(SA)/dr = 2πr -2V/r² = 0

πr³ = V . . . . . multiply by r²/2 and add V

Then the can radius is ...

r = ∛(V/π)

and the height is ...

h = V/(π(V/π)^(2/3)) = ∛(V/π) = r

For the given volume, the dimensions are ...

r = h = ∛(2197/π) ≈ 8.8762 cm

The lightest can with that volume has a radius and height of about 8.88 cm.

_____

<em>Comment on cylinder aspect ratio</em>

You may notice that the lateral area is equal to twice the bottom area for this cylinder. If the can had a top, the minimum weight would be such that the lateral area is twice the total of top and bottom area. In that case, the height is equal to the diameter, not the radius.

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Pls help find the amount at the end of 6 hours

marshall27 [118]

Answer:

A. 7,348

Step-by-step explanation:

P = le^kt

intitial population = 500

time = 4 hrs

end population = 3,000

So we have all these variables and we need to solve for what the end population will be if we change the time to 6 hours. First, we need to find the rate of the growth(k) so we can plug it back in. The given formula shows a exponencial growth formula. (A = Pe^rt) A is end amount, P is start amount, e is a constant that you can probably find on your graphing calculator, r is the rate, and t is time.

A = Pe^rt

3,000 = 500e^r4

now we can solve for r

divide both sides by 500

6 = e^r4

now because the variable is in the exponent, we have to use a log

$log_{e}(6) = 4r$

ln(6) = 4r

we can plug the log into a calculator to get

1.79 = 4r

divide both sides by 4

r = .448

now lets plug it back in

A = 500e^(.448)(6 hrs)

A = 7351.12

This is closest to answer A. 7,348

4 0

3 years ago

• a helicopter hovering at 10 m above the ground is shining a spotlight at a person 30 m away1 . if the person is 2 m tall how l

pshichka [43]

As shown in the figure

Height of helicopter above the ground=30 m

Distance from the base to the point where the person is standing=30 m

height of the person=2 m

Now the person cast the shadow of length x m.

Triangle ABC and triangle EDC are similar.

∵ ∠B= ∠D=90°

∠C is common.

So by AA similarity ΔABC and ΔEDC are similar.

As we know when triangles are similar their sides are proportional.

AB/AD =BC/DC

Let DC=x meter

⇒ $\frac{10}{x}=\frac{30+x}{x}$

⇒5=\frac{30+x}{x}[/tex]

⇒5x=30+x

⇒4x = 30

⇒ x=30/4

⇒ x=7.5 meter

So length of shadow=7.5 meter

2. volume of a sphere of radius r is v (r) = $\frac{4}{3}π r^{3}$

$\frac{\mathrm{d} }{\mathrm{d} r}V$ =4/3π×3 $r^2$

=4π $r^2$

surface area of a sphere of radius r is 4π $r^2$

b) Ratio of derivative of volume of sphere to surface area of sphere= $\frac{4\pi r^2}{4\pi r^2}$

=1 [ incomplete question but you have written few words ]

4 0

2 years ago

What are the solution(s) to the quadratic equation 50 – x2 = 0?

Paraphin [41]

Answer:

No real solution

Step-by-step explanation:

There is no perfect squares in 50

6 0

3 years ago

Read 2 more answers

Which is the graph of g(x) = ⌈x + 3⌉?

77julia77 [94]

ANSWER

$\boxed {D}$

EXPLANATION

The given function is,

$g(x) = ⌈x + 3⌉$

The parent function of this ceiling function is

$g(x) = ⌈x ⌉$

When this function is shifted horizontally 3 units to the left, we obtain the transformed function,

$g(x) = ⌈x + 3⌉$

The correct answer is option D.

See attachment.

6 0

3 years ago

How do i solve 2x+6>20

lukranit [14]

Hello!

To solve 2x+6>20, you'll first need to subtract. First, you'll need to subtract 6 from 20 (20-6). Now if the 6 was negative, you would need to add 6 to 20, but for this equation you'll subtract.

2x>14

Now you will need to divide both sides by 2. Once you've done that you'll have your answer of...

x>7

I hope this helps!

4 0

2 years ago

What are the dimensions of the lightest​ open-top right circular cylindrical can that will hold a volume of 2197 cm cubed​?

What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 2197 cm cubed?