Mathematics: In a scale model of a building, 1 ft represents 60 ft. the volume of the scale model is 18 ft3. what is the volume of the building? the roof of the scale model has a surface area of 4 ft^2. what is the surface area?

No graph so sorry. Is there a graph...

In a scale model of a building, 1 ft represents - id1604882546, derekcalhoun4943

Ответ:

Haddy7202

17.01.2022

$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\$

$\bf \textit{using the volume ratio}\\\\
\cfrac{model}{building}\qquad \cfrac{1}{60}=\cfrac{\sqrt[3]{18}}{\sqrt[3]{v}}\implies \cfrac{1}{60}=\sqrt[3]{\cfrac{18}{v}}\implies \left( \cfrac{1}{60} \right)^3=\cfrac{18}{v}
\\\\\\
\cfrac{1^3}{60^3}=\cfrac{18}{v}\implies v=\cfrac{60^3\cdot 18}{1^3}\\\\
-------------------------------\\\\$

$\bf \textit{using the area ratio}\\\\
\cfrac{model}{building}\qquad \cfrac{1}{60}=\cfrac{\sqrt{4}}{\sqrt{a}}\implies \cfrac{1}{60}=\sqrt{\cfrac{4}{a}}\implies \left( \cfrac{1}{60} \right)^2=\cfrac{4}{a}
\\\\\\
\cfrac{1^2}{60^2}=\cfrac{4}{a}\implies a=\cfrac{60^2\cdot 4}{1^2}$

0,0(0 оценок)

In a scale model of a building, 1 ft represents 60 ft. the volume of the scale model is 18 ft3.
what is the volume of the building?
the roof of the scale model has a surface area of 4 ft^2. what is the surface area?

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question