Question

The volume of a cylinder is given by the formula V = (pi)r^2h, where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius (x - 3) and height (2x + 7). Which expression represents the volume of the can?

Answer 1

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)

Answer 2

Pi(x-3)^2 *(2x + 7)

= 2pi(x)^3 - 5pi(x)^2 - 24pi(x) + 63pi