Use spherical coordinates.
Let H be a solid hemisphere of radius 2 whose density at any point is proportional to its distance from the center of the base. (Let K be the constant of proportionality.)
(a) Find the mass of H.
(b) Find the center of mass of H. (Assume the upper hemisphere of a sphere centered at the origin.)
(c) Find the moment of inertia of H about its axis.

Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.