## Intermediate Algebra (6th Edition)

$(7 \pi y^{3}-42 \pi y^{2} +63 \pi y)$ $cm ^{3}$
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 $(a-b)^{2} = a^{2} -2ab +b^{2}$ $V = 7\pi y (y^{2}-6y+9)$ $cm ^{3}$ $V = (7 \pi y^{3}-42 \pi y^{2} +63 \pi y)$ $cm ^{3}$