How many cubic meters in a cylinder?

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To calculate the volume of a cylinder with a radius of 5 meters and a height of 10 meters, the formula used is V = πr²h. This results in a volume of 785.4 cubic meters. The units confirm that the volume is indeed expressed in cubic meters (m³), as both the radius and height are in meters. The dimensional analysis shows that the volume calculation yields cubic meters, validating the result. The discussion clarifies the correct interpretation of the computed volume.
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Homework Statement



Given a cylinder of radius = 5m, and height = 10m, how many cubic meters is that? If I just compute those values in the formula for a cylinder, I get 785.4. But 785.4 what? Is it785.4m^3?

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LearninDaMath said:

Homework Statement



Given a cylinder of radius = 5m, and height = 10m, how many cubic meters is that? If I just compute those values in the formula for a cylinder, I get 785.4. But 785.4 what? Is it785.4m^3?

Yes, you have a ##\pi r^2h## which dimensionally is ##m^3##.
 
Yes, look at the formula for volume:

V = \pi r^2 h

The units of both r and h are meters, so the units of volume are (meters)^2 * meters = (meters)^3.
 
Thanks jbunniii and LCKurtz
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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