Question

Lucy builds a model of a cylindrical container with volume 5000 cm3. If the scale of the model is 1:30, calculate the volume of the actual container

Answer 1

volume of the model = 5000 cc

$formula \: for \: calculating \: volume \: of \: cylinder \: = \: \pi \times {r}^{2} \times h$

as per the scale each of the radius and height of the cylinder will be 30 times of the model.

IN THE MODEL:

Let the radius = r

height = h

=> Volume = πr²h = 5000 cc

IN THE CYLINDRICAL CONTAINER:

Radius = 30r

Height = 30h

=> Volume = π×(30r)²×30h

= 30³×πr²h

= 30³×5000 cc

= 3³×5×10⁶ cc

= 27×5 m³ [ 1 m³ = 10⁶ cc]

= 135 m³

Hence the volume of the actual cylindrical container is 135 m³.

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