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Question

# A cuboid measuring 3 cm by 5 cm by 2 cm is enlarged by a ratio of 2:1, a) What is the volume of: i) the original cuboid? ii) the enlarged cuboid? b) By what ratio has the volume been increased?

Solution

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Multiply the three dimensions of the cuboid by the given ratio, the dimensions of the enlarged cuboid are:

$\dfrac{2}{1} \times 3 = 6 \text{ cm}$

$\dfrac{2}{1} \times 5 = 10 \text{ cm}$

And,

$\dfrac{2}{1} \times 2 = 4 \text{ cm}$

$\textbf{a)}$

Since the volume of the cuboid is the production of its three dimensions, so:

• The volume of the original cuboid is:

$3 \times 5 \times 2 = \boxed{\color{#c34632}{30 \text{ cm}^{3}}}$

• The volume of the enlarged cuboid is:

$6 \times 10 \times 4 = \boxed{\color{#c34632}{240 \text{ cm}^{3}}}$

$\textbf{b)}$

Divide the volume of the enlarged cuboid by the volume of the original cuboid:

$\dfrac{240}{30} = \dfrac{8}{1}$

So, the volume was enlarged by a ratio $\boxed{\color{#c34632}{8 : 1}}$

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