Question

the mass of a cylinder made of barium with a height of 2 inches depends on the radius of the cylinder as defined by the function (m(r)=7.183pi r^{2}). which system of equations and solution can be used to represent the radius if the mass of the cylinder is 11,000 grams? round to the nearest hundredth of an inch.
(y = 7.183pi r^{2}) and (y = 4; r=0.42) inches
(y = 7.183pi) and (y = r^{2}; r = 4.75) inches
(y = 7.183pi r^{2}) and (y = 11,000; r = 22.07) inches
(y = 7.183r^{2}) and (y=pi; r = 0.66) inches

Explanation:

Step1: Set up the equation

We know that the mass - radius function is $M(r)=7.183\pi r^{2}$, and the mass $M = 11000$ grams. So we set $y = 7.183\pi r^{2}$ and $y = 11000$.

Step2: Solve for $r$

\[

$$\begin{align*} 7.183\pi r^{2}&=11000\\ r^{2}&=\frac{11000}{7.183\pi}\\ r^{2}&=\frac{11000}{7.183\times3.14159}\\ r^{2}&=\frac{11000}{22.564}\\ r^{2}&\approx487.50\\ r&=\sqrt{487.50}\\ r&\approx22.07 \end{align*}$$

\]

Answer:

C. $y = 7.183\pi r^{2}$ and $y = 11000;r\approx22.07$ inches