Answer: The expression that represents the volume of the can (cylinder) is:
V=pi (2x+7) (x-3)^2
V=pi (2x^3-5x^2-24x+63)
Solution:
V=pi r^2 h
Radius of the cylinder: r=(x-3)
Height of the cylinder: h=(2x+7)
Replacing "r" by "(x-3)" and "h" by "(2x+7)" in the formula above:
V= pi (x-3)^2 (2x+7)
V=pi (2x+7) (x-3)^2
V=pi (2x+7) (x^2-2x(3)+3^2)
V=pi (2x+7)(x^2-6x+9)
V=pi ( 2x(x^2)-2x(6x)+2x(9)+7(x^2)-7(6x)+7(9) )
V=pi (2x^3-12x^2+18x+7x^2-42x+63)
V=pi (2x^3-5x^2-24x+63)
The volume of cylinder when radius is (x - 3) and height is (2x + 7) is given by the expression: [tex]\rm V = \pi \times (2x^3-5x^2-24x+63)[/tex] .
Given :
Volume of cylinder - [tex]\rm V = \pi r^2h[/tex]
It is given that the volume of the cylinder - [tex]\rm V = \pi r^2h[/tex]. If the radius is (x-3) and height is (2x+7) than volume of cylinder can be written as:
[tex]\rm V = \pi \times (x-3)^2\times (2x-7)[/tex] --- (1)
Expand the [tex](x-3)^2[/tex] term in equation (1).
[tex]\rm V= \pi \times (x^2-6x + 9)\times (2x+7)[/tex]
Now, multiply [tex](x^2-6x+9)[/tex] and [tex](2x+7)[/tex] in above equation.
[tex]\rm V = \pi\times (2x^3-12x^2+18x+7x^2-42x+63)[/tex]
Further simplify the above equation.
[tex]\rm V = \pi \times(2x^3-5x^2-24x+63)[/tex]
Therefore, the volume of cylinder when radius is (x - 3) and height is (2x + 7) is given by the expression: [tex]\rm V = \pi \times (2x^3-5x^2-24x+63)[/tex].
For more information, refer the link given below
https://brainly.com/question/6071957
