Please explain this. Find the volume of a cylinder with a diameter 5 inches and height 5 feet. (Pi = 22/7)

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- VanillaAngelic

- schrodinger

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- shamim

Make clearer ur question plz!

- mathstudent55

Use this formula:
\(\Large V_{cylinder} = \dfrac{1}{3} \pi r^2 h\)
where r = radius of the base, and h = height of the cylinder.

- mathstudent55

Also, I think you means to use pi = 22/7, not that the radius is 22/7.

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- shamim

I think volume of a cylinder=pi*r^2*h
@mathstudent55

- mathstudent55

LOL. I've been online too long.
Yes, of course you're right.
My formula above is for a cone.

- mathstudent55

\(\Large V_{cylinder} = \pi r^2h\)

- VanillaAngelic

Mind if you explain how do it step by step? Thanks. I really don't understand.

- mathstudent55

Ok. Here is the explanation.
For the formula you need the radius of the base of the cylinder.
You were given the diameter.
Do you know the relationship between the diameter and the radius of a circle?

- VanillaAngelic

No..

- mathstudent55

|dw:1437007341591:dw|

- mathstudent55

A chord of a circle is a line segment that has as its endpoints any two points on the circle.
A chord that passes through the center of a circle is a diameter.
A radius of a circle is a line segment that has the center as an endpoint and a point on the circle as its other endpoint.

- VanillaAngelic

Ok.

- mathstudent55

|dw:1437007540372:dw|

- mathstudent55

As you can see from the circle on the right side, a radius is half the length of a diameter.

- mathstudent55

Now we can back to our problem above.

- mathstudent55

\(\Large V_{cylinder} = \pi r^2 h\)
For pi we will use 22/7 as your problem asks
For h we will use 5 feet
Since the diameter is 5 inches, the radius is 2.5 inches.
We can use all the above info in the formula, but there is one extra step in this case. You have the radius is in inches and the height in feet. We need to choose one of those two units and convert one unit, so both measures are in the same unit.
Let's use inches.
\(\Large V = \dfrac{22}{7} \times (2.5~in.)^2 \times 5~ft \times \dfrac{12~in.}{ft} \)

- mathstudent55

Now we need to calculate the expression above.
\(V = 1178.6~in.^3\)

- VanillaAngelic

Thank you very much!

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