A circular lamina of radius lies in the plane and has surface density kilograms per…

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A circular lamina of radius

3\text{ m}

lies in the plane and has surface density

\sigma(r)=2r

kilograms per square meter, where

r

is the distance from the center in meters. Determine the total mass of the lamina. (a)

27\pi\text{ kg}

(b)

36\pi\text{ kg}

(c)

18\pi\text{ kg}

(d)

54\pi\text{ kg}