QuestionFind the volume of a cylinder with $r=2b$ and $h=5b+3$ using $V=\pi r^{2} h$ in terms of $b$ .

Studdy Solution

STEP 1

Assumptions1. The formula for the volume of a right circular cylinder is $V=\pi r^{} h$ . The radius $r$ is given as $b$
3. The height $h$ is given as $5b+3$

STEP 2

We can substitute the given values of $r$ and $h$ into the volume formula.
$V=\pi (2b)^{2} (5b+)$

STEP 3

implify the expression by squaring $2b$ .
$V=\pi (b^{2}) (5b+3)$

STEP 4

Now we can distribute $4b^{2}$ to $b+3$ .
$V=\pi (20b^{3}+12b^{2})$ So, the volume of the cylinder in terms of $b$ is $20 \pi b^{3}+12 \pi b^{2}$ .

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