Question

The volume of a cylindrical soup can is represented by the expression πr3 + 7πr2, where r is the radius of the cylinder. Which statement best interprets the factor (r + 7) in this context? Hint: The volume of a cylinder is given by the general formula V = πr2h, where h is the height of the cylinder.

Answer 1

π·r^3 + 7·π·r^2 = r^2·π·(r + 7)

r + 7 is the height of the cylinder.

Answer 2

The statement that interpretes the factor (r + 7 ) is that (r+7) is the height of the cylinder

A cylinder is a circular based prism and generally, the volume of a prism is expressed as;

V = bh

where b is the base area and h is the height.

Since cylinder is of circular base

Volume of cylinder = πr²h

The volume of a cylindrical soup is given as

V = πr³ + 7πr²

factor the equation

V = πr² ( r + 7)

relating the equation with V = πr²h

πr² h = πr²( r + 7)

divide both sides by πr²

h = r + 7

Therefore the height of the cylinder is r + 7