Exercise 25 Page 835

A cylindrical can of baked potato chips has a height of 27 centimeters and a radius of 4 centimeters. A new can is advertised as being 30 % larger than the regular can. Both cans have the same radius.

Let h_\text{new} denote the height of the larger can. We can use the formula for the volume of a cylinder.

Cylider	Old	New
Radius	r= 4	r= 4
Height	h= 27	{\color{#009600}{h}}={\color{#009600}{h_\text{new}}}
Volume	V=π r^2 h
	\textcolor{darkorange}{V_\text{old}}=\pi ({\color{#0000FF}{4}})^2({\color{#009600}{27}})=\textcolor{darkorange}{432\pi}	\textcolor{darkviolet}{V_\text{new}}=\pi ({\color{#0000FF}{4}})^2{\color{#009600}{h_\text{new}}}=\textcolor{darkviolet}{16\pi h_\text{new}}

The new can is 30 % larger. This tells us that \textcolor{darkviolet}{V_\text{new}}=130\, \%\cdot\textcolor{darkorange}{V_\text{old}}. Let's use that equation and substitute the known values and expressions to find the value of the height of the new can, h_\text{new}.

\textcolor{darkviolet}{V_\text{new}}=130\, \%\cdot\textcolor{darkorange}{V_\text{old}}

SubstituteII

\textcolor{darkorange}{V_\text{old}}={\color{#0000FF}{\textcolor{darkorange}{432\pi}}}, \textcolor{darkviolet}{V_\text{new}}={\color{#009600}{\textcolor{darkviolet}{16\pi h_\text{new}}}}

\textcolor{darkviolet}{16\pi h_\text{new}}=130\, \%\cdot \textcolor{darkorange}{432\pi}

▼

Solve for h_\text{new}

PercentToFrac

a %=a/100

16\pi h_\text{new}=\dfrac{130}{100}\cdot 432\pi

CalcQuot

Calculate quotient

16\pi h_\text{new}=1.3\cdot 432\pi

Multiply

Multiply

16\pi h_\text{new}=561.6\pi

DivEqn

.LHS /16π.=.RHS /16π.

h_\text{new}=\dfrac{561.6\pi}{16\pi}

ReduceFrac

a/b=.a /π./.b /π.

h_\text{new}=\dfrac{561.6}{16}

CalcQuot

Calculate quotient & Use a calculator

h_\text{new}=35.1

Finally, we get that the height of the new larger can is 35.1 centimeters.