Exercise 37 Page 836

A soy milk container is a rectangular prism with a length of 4 inches, a width of 2 inches, and a height of 9 inches.

A new container is 25 % larger than the old one. Both containers have the same base.

Let h_\text{new} denote the height of the larger container. The volume of a rectangular prism is equal to the product of its dimensions. Now, let's find the volumes of these two containers.

Container	Old	New
Length	l= 4	l= 4
Width	w= 2	w= 2
Height	h= 9	{\color{#FF0000}{h}}={\color{#FF0000}{h_\text{new}}}
Volume	V= l w h
Volume	\textcolor{darkorange}{V_\text{old}}=({\color{#0000FF}{4}})({\color{#009600}{2}})({\color{#FF0000}{27}})=\textcolor{darkorange}{72}	\textcolor{darkviolet}{V_\text{new}}=({\color{#0000FF}{4}})({\color{#009600}{2}}){\color{#FF0000}{h_\text{new}}}=\textcolor{darkviolet}{8 h_\text{new}}

The new container is 25 % larger. This tells us that \textcolor{darkviolet}{V_\text{new}}=125\, \%\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 container, h_\text{new}.

\textcolor{darkviolet}{V_\text{new}}=125\, \%\cdot\textcolor{darkorange}{V_\text{old}}

SubstituteII

\textcolor{darkorange}{V_\text{old}}={\color{#0000FF}{\textcolor{darkorange}{72}}}, \textcolor{darkviolet}{V_\text{new}}={\color{#009600}{\textcolor{darkviolet}{8 h_\text{new}}}}

\textcolor{darkviolet}{8 h_\text{new}}=125\, \%\cdot \textcolor{darkorange}{72}

▼

Solve for h_\text{new}

PercentToFrac

a %=a/100

8h_\text{new}=\dfrac{125}{100}\cdot 72

CalcQuot

Calculate quotient

8h_\text{new}=1.25\cdot 72

CalcQuot

Calculate quotient

8h_\text{new}=90