Answer:
The volume of the cylinder is defined by the expression \(V=\pi (x+8)^2(2x+3)\text{ or }V=\pi (2 x^3 + 35 x^2 + 176 x + 192)\).
Step-by-step explanation:
The volume of a cylinder is given by the formula
\(V=\pi r^2h\)
Where, r is the radius of the cylinder and h is the height.
The radius of the cylinder is (x+8) and the height of the cylinder is (2x+3).
Substitute r = (x+8) and h = (2x+3) in the given formula.
\(V=\pi (x+8)^2(2x+3)\)
\(V=\pi (x^2+16x+64)(2x+3)\) \([\because (a+b)^2=a^2+2ab+b^2]\)
\(V=\pi (2 x^3 + 35 x^2 + 176 x + 192)\)
Therefore volume of the cylinder is defined by the expression \(V=\pi (x+8)^2(2x+3)\text{ or }V=\pi (2 x^3 + 35 x^2 + 176 x + 192)\).
