Chapter 3.8, Problem 2CFU

To determine

To derive: A different proportion from that used in Example 3 relating $x^n$ and y if y varies directly as x.

Answer to Problem 2CFU

  $r=4$

Explanation of Solution

Given information: If y varies directly as x

Calculation:

The volume of a right-circular silo (cylinder) varies directly as its height and the square of its radius. A large silo comes in a standard 30 foot height.

  $V=30k{r}^2$

First: Find the constant of proportionality (k):

  $9420=30\left(k\right)\left({10}^2\right)\to k=3.14$

If the Volume is 9,420 when the radius is 10 feet, find the radius when the volume is 1507.2.

Create a proportion:

  $\begin{array}{l}\frac{30\left(3.14\right)\left(\text{radius}\right)}{\text{volume}}=\frac{30\left(3.14\right)\left(\text{radius}\right)}{\text{volume}}\\ \frac{30\left(3.14\right)\left({10}^2\right)}{9420}=\frac{30\left(3.14\right)\left(r^2\right)}{1507.2}\end{array}$

Solve for r.

  $\begin{array}{l}{r}^2=\frac{150720}{9420}\to r^2=16,\\ r=4.\end{array}$