In: Advanced Math
For the following exercises, write the polynomial function that models the given situation. A cylinder has a radius of x + 2 units and a height of 3 units greater. Express the volume of the cylinder as a polynomial function.
Consider the following for a cylinder,
r = (x + 2)
h = x + 2 + 3
h = x + 5
Consider the formula for volume of a cylinder,
v = πr2h
Put the values in the formula,
v = πr2h
= 22/7 × (x + 2)2(x + 5)
v = 22/7 × (x2 + 4x + 4)(x + 5)
= 22/7 × (x3 + 5x2 + 4x2 + 20x + 4x + 20)
= 22/7(x3 + 9x2 + 24x + 20)
= 22/7x3 + 198/7x2 + 528/7x + 440/7
Hence, the polynomial is 22/7x3 + 198/7x2 + 528/7x + 440/7.
Hence, the polynomial is 22/7x3 + 198/7x2 + 528/7x + 440/7.