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anzhelika [568]
2 years ago
7

If the volume of a cylinder is 72 inches^3, what is the volume of a cone that fits exactly inside the cylinder

Mathematics
2 answers:
garik1379 [7]2 years ago
8 0
<h2>Hello!</h2>

The answer is:

ConeVolume=24in^{3}

<h2>Why?</h2>

Since we know the volume of the cylinder,  and we also know that both cylinder and cone have the same height and same base diameter, we can calculate the volume of a cone that fits exactly inside the cylinder using the following relation:

CylinderVolume=3ConeVolume\\\\ConeVolume=\frac{CylinderVolume}{3}

So, from the statement we know that the volume of the cylinder is  72in^{3}

Then, substituting it into the formula, we have:

ConeVolume=\frac{72in^{3} }{3}=24in^{3}

Have a nice day!

xz_007 [3.2K]2 years ago
5 0

The formula for volume of a cylinder is V = PI x r^2 x h

The formula for the volume of a come is V = PI x r^2 x h/3

Divide the area of the cylinder by 3:

72/3 = 24

The volume of the cone is 24 cubic inches.

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x = 1/3

Step-by-step explanation:

Perform the indicated multiplication:

Clear out the fractions.  The LCD here is 12, so multiply both sides by 12, obtaining:

3(3x - 1) = 24x - 8, or

9x - 3 = 24x - 8

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3 years ago
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3 years ago
Given that x and y are positive integers, solve the equation x² - 4y² = 13​
zvonat [6]
<h3>Answer:  x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

  • A) x-2y = 1 and x+2y = 13
  • B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

\begin{cases}x-2y = 1\\x+2y = 13\end{cases}

Add the equations straight down

  • x+x becomes 2x
  • -2y+2y becomes 0y = 0 which goes away
  • 1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example:  x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

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2 years ago
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Step-by-step explanation:

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Answer:

I suppose it has 4 digits.

Step-by-step explanation:

The fractional equivalent of the repeating decimal would be 15/99.

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