Question

a trophy in the shape of a cup is 40cm high. a miniature mold of the trophy is 12 and a half cm high. if the miniature model of the trophy holds 60ml capacity to the nearest millimetre

Answer 1

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:

$- \( H \) 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.$

We can set up a proportion based on the heights:

$\[\frac{h}{H} = \frac{v}{V}\]$

Given:

- H = 40 cm

- h = 12.5  cm

Substituting the given values into the proportion:

$\[\frac{12.5}{40} = \frac{v}{V}\]$

Now, let's solve for v, the volume of the miniature model:

$\[v = \frac{12.5}{40} \times V\]$

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:

$\[60 = \frac{12.5}{40} \times V\]$

To solve for V:

$\[V = \frac{60 \times 40}{12.5}\]\[V = \frac{2400}{12.5}\]\[V \approx 192\]$

So, the volume of the actual trophy is approximately 192 cm³.