Question

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?

Answer 1

we know that

The volume of a cylinder is given by the formula

`V=3.14 r^(2) h`

where

r is the radius of the cylinder

h is the height of the cylinder

in this problem

`r=x+8\\h=2x+3`

Substitute the values in the formula above

`V=3.14*(x+8)^(2)*(2x+3)`

`V=3.14*(x^(2)+16x+64)*(2x+3) \\ V=3.14 *(2x^(3) +3x^(2) +32x^(2) +48x+128x+192)\\ V=3.14*(2x^(3) +35x^(2) +176x+192)`

therefore

the answer is

The volume of the can is equal to

`V=3.14 *(2x^(3) +35x^(2) +176x+192)\ units ^(3)`