Write an expression for the volume of a cylinder with a height 7in. greater than the radius.

7 π r² + π r³

Explanation:

1) The general formula for the volumen, V, of a cylinder with radius r and height h is:

V = π r² h

2) Now you have the condition that the height is 7 inches greater than the radius, that is:

h = 7 + r

3) Replace h with its expression

V = π r² (7 + r)

4) Expand the product (use distributive property):

V = π (7r²) + π r³ = 7 π r² + π r³

7 π r² + π r³