Chapter 4.5, Problem 26PPE

To determine

Function of amount of juice and height of juice in ounce.

Answer to Problem 26PPE

The function is $V=6.33h$

• h=0.05 in
• V=57 oz

Explanation of Solution

Given data:

Height of glass =10 inch

Volume of glass = 64oz

Formula:

Volume of cylinder= $V=\pi r^{2}h$

Calculation:

As volume of cylinder $V=\pi r^{2}h$

  $\begin{array}{l}64=3.14r^2(10)\\ r=1.427\end{array}$

As the radius of glass is constant and height is varying with volume so,

Function is:

  $\begin{array}{l}V=\pi r^{2}h\\ $ V=\pi {(1.42)}^{2}h$V=6.33h\end{array}$

Height of juice in glass when 47 oz poured out:

  $\begin{array}{l}\text{Volume of juice =64-47}\\ =1\text{7oz}\end{array}$

As,

  $\begin{array}{l}V=6.33h\\ h=\frac{17}{6.33}\\ h=2.68inch\end{array}$

When half of the juice has been poured out,

  $\begin{array}{l}V=\frac{64}{2}\\ V=32oz\end{array}$

  $\begin{array}{l}V=6.33h\\ h=\frac{32}{6.33}\\ h=5.05inch\end{array}$

When height is decreased by 1inch then :

  $\begin{array}{l}h=10-1\\ h=9in\\ so,\\ \text{ V}=\text{6}\text{.33h}\\ \text{ V}=\text{6}\text{.33(9)}\\ \text{ V}=57oz\end{array}$

Conclusion:

The function is $V=6.33h$

h=0.05 in

V=57 oz