Question

The scale factor of a model of a hot air balloon to the actual hot air balloon is 1 to 5. the volume of the actual balloon is 5000 m^3 what is the volume ? A. 0.005 m^3 B.0.025 m^3 C. 40 m^3 D.200 m^3

Answer 1

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

$\bf \cfrac{model}{actual}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{1}{5}=\cfrac{\sqrt[3]{v}}{\sqrt[3]{5000}}\implies \cfrac{1}{5}=\sqrt[3]{\cfrac{v}{5000}} \\\\\\ \left( \cfrac{1}{5} \right)^3=\cfrac{v}{5000}\implies \cfrac{1^3}{5^3}=\cfrac{v}{5000}\implies \cfrac{1}{125}=\cfrac{v}{5000}$

solve for "v"

Answer 2

Answer:

Option C

$40\ m^{3}$

Step-by-step explanation:

Let

x------->  the volume of  the model

y------> he volume of the actual

z------> the scale factor

we know that

The scale factor elevated to the cube is equal to the volume of  the model divided by the volume of the actual

so

$z^{3}=\frac{x}{y}$

we have

$z=1/5, y=5,000\ m^{3}$

substitute and solve for x

$(1/5)^{3}=\frac{x}{5,000}$

$x=5,000(1/5)^{3}$

$x=40\ m^{3}$