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3 years ago

If a cone has a height that equals twice the diameter of its base,what is its volume in terms of the height

Mathematics

1 answer:

Andrew [12]3 years ago

4 0

I am not sure. that is too confusing for my little brain

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A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

6 0

3 years ago

wallace has a $50 bill. pizza pies cost 12.25 each. if p represents the number of pizzas he buys, write an expression for the ch

Stolb23 [73]

Since he has to give 50, and 12.25*p is the amount of money he has to spend (since it's 12.25 per pizza), we have 50-12.25=change

5 0

3 years ago

PLEASE HELP!! FILL IN THE BLANK MATH QUESTION, ONLY ANSWER IF YOU KNOW THE CORRECT ANSWER CAUSE MY GRADE DEPENDS ON IT

vagabundo [1.1K]

First blank: sin. C = h/a
The ratio for sin. is opposite (the height) over hypotenuse (a).

Second blank: Area = (1/2)b(a sin. C)
In this substitution, we are substituting the value of h into the traditional area of a triangle formula.

Third Blank: Area = (1/2)ab(sin C)
We are using the commutative property to move the position of a.
Hope this helps and good luck in your classes!

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3 years ago

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3 years ago

1 1/3 x 1/14<br> Help please

nikklg [1K]

Step-by-step explanation: