we know that
The volume of a cylinder is given by the formula
[tex] V=\pi r^{2} h [/tex]
where
r is the radius of the cylinder
h is the height of the cylinder
in this problem
[tex] r=x+8\\ h=2x+3 [/tex]
Substitute the values in the formula above
[tex] V=\pi*(x+8)^{2}*(2x+3) [/tex]
[tex] V=\pi*(x^{2}+16x+64)*(2x+3) \\ V=\pi *(2x^{3} +3x^{2} +32x^{2} +48x+128x+192)\\ V=\pi *(2x^{3} +35x^{2} +176x+192) [/tex]
therefore
the answer is
The volume of the can is equal to
[tex] V=\pi *(2x^{3} +35x^{2} +176x+192) units ^{3} [/tex]
Answer:
The volume of the cylinder is defined by the expression [tex]V=\pi (x+8)^2(2x+3)\text{ or }V=\pi (2 x^3 + 35 x^2 + 176 x + 192)[/tex].
Step-by-step explanation:
The volume of a cylinder is given by the formula
[tex]V=\pi r^2h[/tex]
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.
[tex]V=\pi (x+8)^2(2x+3)[/tex]
[tex]V=\pi (x^2+16x+64)(2x+3)[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]V=\pi (2 x^3 + 35 x^2 + 176 x + 192)[/tex]
Therefore volume of the cylinder is defined by the expression [tex]V=\pi (x+8)^2(2x+3)\text{ or }V=\pi (2 x^3 + 35 x^2 + 176 x + 192)[/tex].
