What is the approximate volume of a tree trunk is the trunk is 12 feet tall with a circumference of 4.5

1 answer:

4 0

We need to solve for the radius
circumference = radius * 2 * PI
radius = circumference / (2*PI)
radius = 4.5 / ( 6.2831853072 )
radius = 0.7161972439 feet
Formula for cylinder volume:
Volume = π • r² • height
Volume = π • ( 0.7161972439)^2 * 12
Volume = PI * 0.5129384922 * 12
Volume 19.3373255857 cubic feet

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If f'(x)=2/x and f(sqrt(e))=5, then f(e)=

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$f'(x)=\dfrac2x$
$\implies f(x)=\displaystyle\frac2x\,\mathrm dx=2\ln|x|+C$

$f(\sqrt e)=5\implies 5=2\ln|\sqrt e|+C$
$\implies 5=\dfrac22\ln e+C$
$\implies C=4$
$\implies f(x)=2\ln|x|+4$
$\implies f(e)=2\ln|e|+4=6$