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

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