## Related questions with answers

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

VerifiedMultiply 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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