#### Answer

$(7 \pi y^{3}-42 \pi y^{2} +63 \pi y) $ $cm ^{3}$

#### Work Step by Step

Given,
Radius $(r) = y-3$ cm
Height $(h) = 7y$ cm
Volume of the cylinder $V = \pi r^{2} h$
$V = \pi (y-3)^{2} \times 7y$ $cm ^{3}$
$V = 7\pi y (y-3)^{2} $ $cm ^{3}$
Using $(a-b)^{2} = a^{2} -2ab +b^{2} $
$V = 7\pi y (y^{2}-6y+9) $ $cm ^{3}$
$V = (7 \pi y^{3}-42 \pi y^{2} +63 \pi y) $ $cm ^{3}$