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Question

# A cube of side 4 cm is enlarged by a ratio of 3:1. a) What is the volume of: i) the original cube? ii) the enlarged cube? b) By what ratio has the volume been increased?

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Multiply the side length of the cube by the given ratio, the side length of the enlarged cube is:

$\dfrac{3}{1} \times 4 = 12 \text{ cm}$

$\textbf{a)}$

Since the volume of the cube is the cube of its side length, so:

• The volume of the original cube is:

$4^{3} = \boxed{\color{#c34632}{64 \text{ cm}^{3}}}$

• The volume of the enlarged cube is:

$12^{3} = \boxed{\color{#c34632}{1728 \text{ cm}^{3}}}$

$\textbf{b)}$

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

$\dfrac{1728}{64} = \dfrac{27}{1}$

So, the volume was enlarged by a ratio $\boxed{\color{#c34632}{27 : 1}}$

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