Answer:
the volume of the actual trophy is approximately 192 cm³
Step-by-step explanation:
To find the capacity of the miniature model of the trophy, we can use ratios.
Let's denote:
[tex]- \( H \) as the height of the actual trophy (40 cm).\\- \( h \) as the height of the miniature model (12.5 cm).\\- \( V \) as the volume of the actual trophy.\\- \( v \) as the volume of the miniature model.[/tex]
We can set up a proportion based on the heights:
[tex]\[\frac{h}{H} = \frac{v}{V}\][/tex]
Given:
- H = 40 cm
- h = 12.5 cm
Substituting the given values into the proportion:
[tex]\[\frac{12.5}{40} = \frac{v}{V}\][/tex]
Now, let's solve for v, the volume of the miniature model:
[tex]\[v = \frac{12.5}{40} \times V\][/tex]
The volume of the miniature model v is given as 60 ml.
However, we need to convert 60 ml to cubic centimeters (cm³) since the height was given in centimeters.
1 milliliter (ml) is equal to 1 cubic centimeter (cm³).
So, v = 60 ml = 60 cm³.
Now we can solve for V, the volume of the actual trophy:
[tex]\[60 = \frac{12.5}{40} \times V\][/tex]
To solve for V:
[tex]\[V = \frac{60 \times 40}{12.5}\]\[V = \frac{2400}{12.5}\]\[V \approx 192\][/tex]
So, the volume of the actual trophy is approximately 192 cm³.
