Find the mass of a cylindrical rod with a radius of 5 centimeters and a length of 30 centimeters, made of two metals in such a way that the density of the rod × centimeters from the left end is $\rho ( x ) = 10 - 0.05 x$ grams per cubic centimeter.
A) 6525 $\pi$
B) 6975.5 $\pi$
C) 6937.5 $\pi$
D) 6637.5 $\pi$

Question

Quizplus · Accepted Answer

The mass of the rod is found by integrating the density function over the length of the rod. The volume element is $\pi r^2 dx$, where $r = 5$. The integral is $\int_0^{30} (10 - 0.05x) \pi (5^2) dx$, which evaluates to 6937.5 $\pi$.

Find the Mass of a Cylindrical Rod with a Radius ρ(x)=10−0.05x\rho ( x ) = 10 - 0.05 xρ(x)=10−0.05x

Find the Mass of a Cylindrical Rod with a Radius $\rho ( x ) = 10 - 0.05 x$