The volume of a cylinder is given by the formula v=3.14r^2h, where r is the radius of the cylinder and h is the height. suppose a cylindrical can has radius (x 8) and height (2x 3). which expression represents the volume of the can?

area of the cylinder is πr² and height is h

π = 3.14

since volume is area x volume

the formula used to find the volume of the cylinder is

V = 3.14r²h

where r - radius - x + 8

h - height - 2x + 3

substituting these values in the equation

V = 3.14 * (x + 8) ² x (2x + 3)

expanding the brackets

V = 3.14 * (x² + 16x + 64) x (2x + 3)

V = 3.14 (2x³ + 32x + 128 + 3x² + 48x + 192)

adding the like terms

V = 3.14 (2x³ + 3x² + 80x + 320)

V = 3.14 (x + 8) ^2 (2x + 3) = 3.14 (x^2 + 16x + 64) (2x + 3)